Obtaining accurate rainfall measurements is highly important in urban areas, having a significant impact on different aspects in city life. Opportunistic rainfall sensing utilizing measurements collected by existing microwave and mmWave-based wireless networks has been researched in the last two decades and can be considered as an opportunistic integrated sensing and communication (ISAC) approach. In this paper, we compare two methods that utilize received signal level (RSL) measurements obtained by an existing smart-city wireless network deployed in the city of Rehovot, Israel, for rain estimation. The first method is a model-based approach using the RSL measurements from short links, in which two design parameters are calibrated empirically. This method is combined with a known wet/dry classification method, which is based on the rolling standard deviation of the RSL. The second method is a data-driven approach, based on a recurrent neural network (RNN), which is trained to estimate rainfall and classify wet/dry periods. We compare the results of rainfall classification and estimation from both methods and show that the data-driven approach slightly outperforms the empirical model and that the improvement is most significant for light rainfall events. Furthermore, we apply both methods to construct high-resolution 2D maps of accumulated rainfall in the city of Rehovot. The ground-level rainfall maps constructed over the city area are compared for the first time with weather radar rainfall maps obtained from the Israeli Meteorological Service (IMS). The rain maps generated by the smart-city network are found to be in agreement with the average rainfall depth obtained from the radar, demonstrating the potential of using existing smart-city networks as a source for constructing 2D high-resolution rainfall maps. Accurate and robust rainfall measurements are highly important for urban water management, flood risk mitigation, urban planning, transportation management, agriculture and more.Flash floods can be caused by excessive rainfall and are characterized by rapid onset. The presence of large impervious areas, buildings and blocking of storm-water flow impose high risks of flash floods in urban areas. Flash floods are frequently responsible for loss of lives and damage to infrastructure. Climate change and increasing urbanization implies more frequent and severe flash floods in the future. Over the last decade, flash-flood forecast lead-time has expanded up to six hours due to improved rainfall forecasts; yet, unknown future precipitation remains the largest source of uncertainty of flash-flood forecasts . Javier The absorption and scattering of electromagnetic waves from hydrometeors along the path of propagation cause attenuation to transmitted signals. This fact was utilized for the first time by Messer et al.  in 2006 The rapid growth of urbanization and population, in addition to advancements in communication technology, have promoted the concept of smart cities, which support city operations intelligently with minimal human interaction . As smarSmart cities provide local municipalities with broadband networks using optical fibers and/or millimeter wave links to support high-bandwidth communication. These networks provide infrastructure for wireless WIFI network solutions, communication of public and education buildings, connection to security cameras and more. Signals transmitted in the E-band frequency range (60 GHz to 90 GHz) provide high bandwidth but do not penetrate easily through buildings and can be attenuated by foliage and rain to a large extent .Due to these limitation, E-band links are usually used for short-range communication. These short links are also common in the wireless backhaul of emerging 5G cellular networks. Such networks can have dense coverage over urban areas, which brings up great opportunities to obtain high-resolution rainfall maps.Similar to the use of CMLs from cellular backhaul networks to serve as meteorological sensors, smart-city wireless links can be exploited, as well, to provide opportunistic meteorological sensing abilities from dense urban areas without the additional cost of placing dedicated rain measuring devices.t indicates time.The network hardware reports the CMLs’ transmitted signal level (TSL) of the transmitter and the received signal level (RSL) of the receiver, which are usually logged by network operators for network management purposes (or can be accessed directly using the simple network management protocol (SNMP)). The attenuation of the transmitted signal is, therefore, obtained by:As mentioned before, the transmitted signal is scattered by hydrometeors along the path of propagation, which constitutes the rain-induced attenuation of the signal. The total attenuation of a signal is modeled as a summation of free-space attenuation (“path loss”), gaseous attenuation, rain induced attenuation and more.To summarize, total attenuation model of :(2)A(t)=a effect  and ABLAr(t)ribution ; L, in kA comprehensive study on rainfall and water vapor sensing with microwave links operating at E-band frequencies was conducted in . The autIt was shown in  that theIn our previous work , we presIn this paper, we compare two methods of rainfall estimation from the attenuation measurements of short E-band links: the first is a two-parameter empirical model from , which c1.We present a comparison between an empirical short links model and an RNN-based data-driven approach for rainfall estimation from RSL measurements. We show that although the RNN-based approach performs better in terms of RMSE, the simple short links model yields similar results for moderate and strong rain intensities (higher than 5 mm/h), despite being much simpler.2.We create high-resolution 2D maps of 24 h-accumulated rainfall, which are constructed from the estimates of either method. The constructed maps are compared against rainfall maps provided by the IMS weather radar, and both show good agreement with the ground truth.The main contributions of this paper are:The rest of this paper is organized as follows: https://www.smbit.co.il). The network consists of 66 links, where each link contains 2 sub-links for the two opposite directions. All links operate in the E-Band frequency range, namely, in the range of 70 GHz to 84 GHz, while the majority of links operate at 74.375 GHz. The RSL values are sampled every 30 s with a quantization level of 1 dB. The TSL is not recorded and is assumed to be constant.RSL measurements from the smart-city network of Rehovot are recorded regularly by the network operator company SMBIT LTD ) in the northern part of the city is used for validation and marked as ‘RG’ in A rain gauge , The Hebrew University of Jerusalem. Examples of RSL time-series raw data from links 29, 2, 4, 5 and 16 are shown in the top five panels of We noticed some changes in the RSL properties of some links at different years, such as different baseline levels and even changes in the range of attenuation values due to rain. Some links showed more than a 10 dB difference between the median of the winter RSL of 2021 and the winter RSL of 2020. Furthermore, links that were too short showed only small attenuation values of the RSL during rainfall, and others were not attenuated at all. We excluded those links, as well as links showing large fluctuations during dry periods. The excluded links are shown as dashed lines in The full dataset, consisting of RSL measurements from a fixed number of links is split into three datasets. The first one is used for training the network (TRAIN). The second one is used for validation and hyper-parameter tuning (VALIDATION). The last one is used for testing only (TEST).The TRAIN set consists of data from different rain events that occurred during 1 October 2019 to 31 March 2020.The VALIDATION set consists of data from different rain events that occurred during 1 November 2020 to 31 December 2020.The TEST set consists of data from different rain events that occurred during 1 January 2021 to 28 February 2021.The datasets’ durations are summarized in Since, most of the time, the weather in Israel is not rainy, the datasets are imbalanced toward dry periods. The wet and dry samples ratio are summarized in The wet samples are also imbalanced toward light rainfall, as can be seen in In this section, we compare the two methods of estimating the path-averaged rainfall rate. The first method we use is the empirical short links model from , which uThe empirical short links model from  is used ucted in . The obst, of link i. i.The model has two parameters (unique per link), which are used to correct the short-links-related inaccuracies. The model is defined as follows:i, i and the long link, respectively.The model parameters are estimated by minimizing the following cost function:The wet/dry classification method from  is used  work of  and was  work of . A scaliIn the next sections, we use the short links model and the RSD method together for wet/dry classification and rainfall estimation and refer to it as the “SLM-RSD” model, which stands for short links model—rolling standard deviation.n is defined as follows:n; w is a fixed window size, which is the ratio between the sampling rate of the rain gauge and the sampling rate of the RSL; L is the link’s path length; and F is the link’s frequency. In our case, w is set to 20 since the rain gauge is measured every 10 min, whereas the RSL is sampled every 30 s. In this way, The input of the network includes both the RSL measurements and the corresponding length and frequency of each link. The RSL measurements are sampled every 30 s, whereas the rain-gauge measurements are sampled every 10 min. A single input to the network at time-step The RSL measurements of each link are normalized by subtracting the median value of the entire RSL time series for the given link:L (representing The network is trained to classify an input sequence of non-overlapping vectors containing samples of the form  to a seqThe architecture of the combined rain estimation and classification network is depicted in The selection of The RH consists of fully connected (FC) layers followed by ReLU activation, and the WD block consists of one layer of FC followed by sigmoid activation. A skip connection, which concatenates the input, Four configurations were tested, where we changed the RH size and also enabled the skip connection, which concatenates the network’s input to the GRU output before applying the rain head. The different configurations are described in i and ground truth measurements The loss function includes a regression term, which is a mean squared error (MSE) loss, and a classification term, which applies focal loss  to the wThe data were augmented by letting the input sequences start at a random point at the beginning of each epoch. The random starting point is selected uniformly from To evaluate the classification results, we use true positives (TPs), false positives (FPs), true negatives (TNs) and false negatives (FNs) as the basis for other useful classification metrics.The first metric we used is the overall accuracy, which is defined as:Since the data are imbalanced toward dry samples, and since the more challenging task is identifying wet periods, precision  and recaThe balanced accuracy is also used for the same reasons, where it is defined by the average of the true positive rate and the true negative rate.To validate the rainfall estimation results, the normalized bias (NBIAS) and normalized RMSE (NRMSE) are used:A GRU with 2 layers and a hidden layer with 256 neurons were used. The model was trained with sequence lengths of 8 h, which is equivalent to the length of 48 samples. ADAM optimizer  was usedWe compared the performances of the different architectures on the TEST dataset. The results are summarized in The four configurations produce similar results in terms of the classification metrics. All configurations perform better than the SLM-RSD model in terms of RMSE and F1 score. From now on, we continue the results section with the “Large RH + Skip” configuration and refer to it as, simply, “RNN”.We compared the receiver operating characteristic (ROC) curves and their respective area under curve (AUC) of the RNN models to the SLM-RSD model on the TEST dataset in The performance of both rainfall estimation methods are depicted in W parameter for these specific links.Inspecting the performance of individual links, the short links model performed slightly better on links 1, 2, 22 and 40, while the RNN model performed better on the rest. Links 26 and 28 exhibit overestimation using the short links model, which can be explained by a non-optimal The performances of the models in terms of the NBIAS and NRMSE for different values of rainfall intensity are presented in The RNN model achieves lower RMSE than the SLM-RSD model for all ranges of rainfall intensity. The major improvement in the RNN method is achieved at low rainfall intensities. For rain rates larger than 5 mm/h, the RNN method performs slightly better. Estimating light rainfall is obviously a harder task than estimating strong rainfall since the range in the attenuation values are smaller and closer to the quantization noise of the RSL signal. Therefore, the RNN model outperforms the short links model for light rainfall as expected.An example of the combined wet/dry classification and rainfall estimation results on the TEST dataset for link 2 is shown in In this subsection, we construct high-resolution 2D maps of 24 h-accumulated rainfall and compare the results to the rain-gauge-adjusted weather radar maps of the Israeli Meteorological Services (IMSs).i, i; D, in km, is the radius of influence, i.e., the distance beyond which a link ceases to effect target point We apply inverse distance weighting (IDW) interpolation, as described in , to consThe 24 h-accumulated rainfall maps obtained from both methods are compared to the IMS-adjusted weather radar in In most cases, the estimated rain maps show an agreement with the average rainfall depth of the adjusted radar, indicating that the method is able to distinguish between light and strong rainfalls.A comparison between the estimated and the adjusted radar maps using BIAS and RMSE was made. The metrics are calculated over the locations where the estimated values are available, i.e., up to 2 km distance from the center of the closest link. In this paper, we conducted a comparison between two methods of rain estimation from RSL measurements of an existing smart-city network operating at E-band frequencies. The first method is based on a calibration process, where every link is assigned two parameters that are estimated from attenuation measurements of a reference link in the network. The second method is based on an RNN model, where we trained a set of links to detect wet and dry periods and estimate the rainfall intensity based on rain-gauge measurements, which serve as the ground truth.When looking at the rain estimation results for a given link, the RNN-based network provided better results in terms of RMSE compared to the short links model, but the improvement itself was less than 20% in average performance, and the largest difference was achieved at lower rainfall intensities. This indicates that a simple  linear model can be used for medium to strong rainfalls.A comparison of the estimated rain maps with the IMS radar maps when accumulated over 24 h resulted in low spatial correlation for both methods. However, the estimated maps show an agreement with the average intensity of the radar, and the two methods are able to distinguish between light and strong rainfalls, as well as produce maps with higher spatial resolution (with respect to the radar). Differences between the estimated maps and the radar maps can arise from changes in the rainfall intensity at different altitudes. The links measure the rainfall at street level, whereas the radar measures the rain at much higher altitude. In addition, the quantization of the RSL and errors in the baseline determination and the wet/dry classification also contribute to the differences between the maps.Filtering out problematic links is a crucial step before constructing the rainfall maps. Noisy links with large fluctuations in the RSL can yield overestimation. The overestimation is prominent when the rainfall is accumulated for long periods, and this is directly related to the performance of the wet/dry classifier. The change in the RSL properties of some links between different years resulted in poor performance of both the short links model and the RNN. Therefore, a more frequent estimation of the model parameters should be performed.


Orthogonal time frequency space (OTFS) is a novel modulation scheme that enables reliable communication in high-mobility environments. In this paper, we propose a Transformer-based channel estimation method for OTFS systems. Initially, the threshold method is utilized to obtain preliminary channel estimation results. To further enhance the channel estimation, we leverage the inherent temporal correlation between channels, and a new method of channel response prediction is performed. To enhance the accuracy of the preliminary results, we utilize a specialized Transformer neural network designed for processing time series data for refinement. The simulation results demonstrate that our proposed scheme outperforms the threshold method and other deep learning (DL) methods in terms of normalized mean squared error and bit error rate. Additionally, the temporal complexity and spatial complexity of different DL models are compared. The results indicate that our proposed algorithm achieves superior accuracy while maintaining an acceptable computational complexity. Currently, orthogonal frequency division multiplexing (OFDM) is the main communication modulation technique used in long-term evolution (LTE) and fifth-generation 5G) systems because of its excellent spectrum utilization . HoweverG systemsAccurately estimating the channel in the delay-Doppler (DD) domain is crucial for successful signal detection at the receiver. In , the autDeep learning (DL) has experienced significant advancements in image and speech recognition, and its application has extended to the field of communication in recent years . In 14]14], the In this work, we employ a predictive approach to enhance the performance of channel estimation by considering the implied time correlation. By capturing and utilizing this time correlation information, we aim to make predictions about the channel state and improve the accuracy of the estimation process. First, we obtain preliminary channel estimation results by using the algorithm in the literature . The preThe OTFS modulation block diagram is shown in After that, From , the chaThe Wigner transform converts the received signal, From (1)–(7), we can obtain the input–output relationship formula in the DD domain: Doppler . In thisThe pilot placement of the threshold scheme in  is shownWe can rewrite the input–output relationship of the pilot according to (8) asAt the receiver, for the channel estimation part, The BER is also a measure of channel estimation performance. We assume that in the received signal, Our proposed Transformer estimation structure is shown in In , a transIn the encoder, the time series data Then, the positional encoding information is added to the output of the input layer. Concatenating these vectors together yields a matrix, ector, v :(14)qt=WMatrices The multi-headed attention mechanism is the integration of multiple independent attention modules, which is similar to multiple convolutional kernels in convolutional neural networks (CNN) to help the network extract richer features:The results obtained from the multi-attention mechanism are subjected to residual connection layer and layer normalization operations to obtain the final outputs. In , ResNet The proposed Transformer estimation algorithm training process can be described as follows: The inputs of the training data are the results of the conventional channel estimation algorithm, and the labels are actual channel responses. Because the channel response is a complex form, our training data splices the real and imaginary parts together. The channel responses from the previous In the training phase, the mean square error (MSE) is selected as the loss function :(19)JMSEaptively . The sizIn this section, the simulation results of our proposed algorithm are given to verify the better performance than the threshold method and other deep learning methods. The parameters of our simulation are given in The NMSE of our channel estimation method is computed asIn In In Space and time are two important metrics for evaluating the computational complexity of a DL model. In this paper, the quantity of parameters is chosen as the space evaluation metric, and the quantity of floating-point operations (FLOPs) is selected for the time aspect. As the number of parameters in a model increase, it necessitates a larger amount of data to effectively train the model. However, this can lead to a higher risk of overfitting, where the model becomes overly specialized to the training data. Additionally, excessive time complexity can significantly prolong the training and prediction processes.i-th hidden layer, respectively.The quantity of parameters refers to how many parameters the model contains and directly ascertains the size of the model. Usually, the parametric quantities of a model are analyzed to determine the memory usage of a computer. Assuming that the DL models contain multiple hidden layers, the formula for calculating the quantity of parameters for DNN, RNN, LSTM, and Transformer can be written respectively asThe Transformer estimation model constructed in The quantity of FLOPs can be understood as the amount of computation, which is used to measure the complexity of the model time. Individual FLOPs generally refer to a single addition, subtraction, multiplication, or division operation. In neural networks, since the number of operations of the activation function is very small, it is not considered in FLOPs. Assuming that the DL models contain multiple hidden layers, the formula for calculating the quantity of FLOPs for DNN, RNN, LSTM, and Transformer can be written, respectively, asThe number of FLOPs for a fully connected layer in the Transformer estimation model can be written asIn this paper, we focus on exploring the channel estimation algorithm for OTFS systems and propose a novel approach that incorporates the Transformer model. The inclusion of Transformer in our work stems from its exceptional capability to handle time series data more effectively when compared to other neural network architectures. Initially, we employ the threshold method to obtain preliminary channel estimation results. However, in order to achieve superior channel estimation performance, we consider the inherent temporal correlation present in channel responses. To leverage this correlation, we treat the data as time series and utilize them for predicting channel responses. The proposed Transformer estimation algorithm demonstrates better NMSE and BER performance than the threshold method proposed in the literature and conventional neural networks under the same


Preclinical dosimetry is essential for guiding the design of animal radiopharmaceutical biodistribution, imaging, and therapy experiments, evaluating efficacy and/or toxicities in such experiments, ensuring compliance with ethical standards for animal research, and providing reasonable initial estimates of normal-organ doses in humans, required for clinical translation of new radiopharmaceuticals. This MIB guide provides a basic protocol for obtaining preclinical dosimetry estimates with organ-level dosimetry software. Preclinical dosimetry largely comprises two paradigms: 1) small-animal dosimetry, wherein rodent dose estimates are derived and 2) translational dosimetry, wherein prospective human dosimetry estimates are derived from animal biodistribution data. Several examples of the applications of these respective paradigms are described below.Internal dosimetry entails the determination of the absorbed dose delivered to humans or animals from imaging as well as therapeutic radiopharmaceuticals. It thus serves as an “indicator” of the probability and/or severity of the radiation-related biological effects of administered radiopharmaceuticals. ex vivo gamma counting measurements, dosimetry can also help ensure the planned administered activity is unlikely to cause radiogenic toxicities that may perturb the study output. In particular, this can be important in experiments utilizing engineered mouse models that have deficient or absent DNA repair mechanisms and are therefore highly radiosensitive . Dosimetry is also valuable for ensuring compliance with ethical standards for animal research – for example, minimizing pain in experimental animals.Small-animal dosimetry is valuable in assessing and managing radiation exposures to laboratory animals used in preclinical studies. For preclinical radiopharmaceutical therapy, dosimetry provides a meaningful basis on which to assess or predict efficacy, toxicities, and therapeutic ratios . Frequently, it is employed in the design of radiopharmaceutical therapy studies to estimate the administered activities required to induce a demonstrable tumor response without exceeding tolerable doses for at-risk organs. The number of animals needed to characterize such radiopharmaceuticals can thereby be minimized while still yielding useful dose-response data. For small-animal biodistribution studies, including those utilizing PET, SPECT, and/or de jure or de facto) that human dosimetry estimates be extrapolated from animal models prior to human administration of radiopharmaceuticals; such estimates accompany translational mechanisms such as investigational new drug applications. Translational dosimetry estimates can also be valuable at the early stages of radiopharmaceutical development – for example, in identifying candidate radiopharmaceuticals for further development or for theranostic applications.The chief role of translational dosimetry is to satisfy regulatory requirements for clinical translation of new radiopharmaceuticals as well as to avoid excessively high doses in human research subjects or patients. The FDA and other regulatory bodies typically mandate  from estimates of the number of nuclear transformations that occur within source regions  after administration of the radiopharmaceutical. The reader is strongly encouraged to refer to the MIRD Primer1 for a detailed examination of the fundamental principles of this schema. The essential dosimetric quantities of absorbed dose and effective dose are defined below.The basic protocol described is for organ-level dosimetry, and utilizes the mathematical framework of the MIRD schemaThe absorbed dose . The effective dose coefficient The effective dose [Sv] is used as a single-value metric of the risk  of radiation-induced stochastic effects in reference humans. It is a weighted sum of the equivalent doses to various organs and tissues of the human body, where the weighting factors reflect the relative sensitivity of each tissue to radiation-induced cancer or germ-cell mutagnesisFor considering deterministic effects such as therapy  or tissue reactions , the absorbed dose can also be weighted by an appropriate relative biological effectiveness (RBE) factor for different radiation types:2 There is no current consensus on the values of This utilization of RBE parallels the concept of the radiation weighting factor used in Numerous software tools are available to facilitate organ-level dosimetry computations in animal or human phantoms . Most coThe basic approach of this protocol is to obtain an organ-level dosimetry estimate starting from animal biodistribution data routinely quantified in units such as standard uptake value (SUV) or percent of the administered activity per gram (%IA/g) with the use of widely available organ-level dosimetry software tools which can perform curve-fitting and integration of time-activity data and the dose calculation . ImportaBiological uptake or clearance: uptake or clearance of a radionuclide by biological processes that are independent of the physical decay of the radionuclide.Effective uptake or clearance: net uptake or clearance of a radionuclide by a combination of radioactive decay and biological processes.Standardized uptake value (SUV): a measure of activity concentration in an organ or tissue region, which is decay-corrected to time of administration and normalized to total body mass, that is, activity per unit mass of tissue divided by the activity administered per unit body mass.Subject anatomy  is generally assumed to be time-invariant and is matched to a standard reference anatomic phantom used for the dosimetry calculations.The radionuclide is homogeneously distributed with the respective source regions The radionuclide’s emissions, in terms of their respective frequencies and energies, occur according to established decay schemesNo radioactive progeny are generated by the decay of the radionuclideThe biodistribution, quantified in units of SUV, is equivalent among species and subjects of different total-body masses and the computational phantoms used to represent them.Tissue harvested for biodistribution measurements include the tissue parenchyma and blood .Prior to performing biodistribution measurements, the investigator should familiarize themselves with the pertinent phantoms  and software that will be used in the dosimetry computation software to ensure the tissues to be assayed are consistent with the source-regions defined in the phantom and the software. Regardless of the software chosen, the investigator is strongly encouraged to thoroughly read its documentation and/or manual.Biodistribution measurements identify the regions of the body where activity accumulates and establish how the activity changes over time in these regions. There are several key study design considerations for biodistribution measurements: 1) What measurement technique will be used? 2) What regions will be analyzed? 3) At what time points post-administration will measurements be performed? 4) How many animals will be used?ex vivo radiometric counting  of tissues harvested from small animals or by segmentation of serially acquired small-animal PET, SPECT, or planar gamma camera images. Ex vivo counting is considered the ‘gold standard’ for organ-level dosimetry, primarily due to its high sensitivity, quantitative accuracy, simplicity, and reproducibility. Additionally, for small-animal imaging anesthesia is required at each measurement time point and may impact the data thus measured. Therefore, this Guide recommends ex vivo measurements. This approach, however, requires a larger number of animals, as a statistically reliable number of animals  must be sacrificed at each measurement time point, and is generally more time-consuming and labor-intensive than imaging-based biodistribution studies.In the preclinical setting, activity quantification is usually performed by either a priori understanding of the radiopharmaceutical, including organ(s) of likely highest uptake, excretion route, metabolism and likely biodistribution and excretion route of radiometabolites. At minimum, the source regions sampled should include those exhibiting the highest activity concentrations, radiosensitive tissues with demonstrable accumulation or retention, blood, contents of the major excretory pathways , and the whole body or animal carcass . To ensure that all activity can be accounted for, it is also advisable to measure the activity present in the bedding material that contains the animal excreta.17 However, it is often difficult to impossible to quantitatively recover all of the activity administered unless animals are housed individually in metabolic cages, but this is rarely done in practice.Selection of anatomic regions for analysis should be based on available data or an An essential consideration in study design is the number and temporal spacing of the biodistribution samples. Ideally, biodistribution should be sampled at a sufficient number of time points which are temporally spaced such that the uncertainty in the TIAC is minimized (see Step 4); this can usually be accomplished by ensuring that each component of uptake and clearance can be identified. Since various source regions may exhibit distinct uptake and clearance patterns, it is challenging to determine time points that are simultaneously optimal for all such regions, especially in light of logistical considerations such as the rapid decay of short-lived radionuclides, cost, and limitations on animal cohort size. The ICRU has proposed that time points be selected based on multiples of the effective half-life, Using a larger sample size will typically increase the precision of the dosimetry estimates. Realistically, the number of time points and the number of animals per time point should be chosen based on several factors such as the research question, resources available, animal welfare considerations, and the expected variability in the data. For dosimetry purposes, it is generally preferable to obtain fewer replicates  at more time points rather than vice versa.A minimum of 4 time points is recommended for adequate temporal resolution of the time-activity curve. A minimum of 3–4 animals per time point is recommended for adequate statistical power for the tissue activity measurements. For statistical rigor in curve-fitting of time-activity data, a degree of freedom  of at least 1 is required. For example, for a bi-exponential curve, with 2 zero-time intercepts and 2 clearance constants and therefore a total of 4 fittable parameters, at least 5 time points would be required. In practice, however, such statistical rigor is often sacrificed.3 for soft tissues) to obtain the mass concentration.The SUV is a measure of activity concentration in a region, which is decay-corrected to the time of administration and normalized to total body mass:Finally, the mean SUV among the animal subjects at each time point is computed. If the animal body masses are reasonably consistent across the study population, the mean SUV can be approximated using the animal population mean body mass, Standard deviations of the mean values of the respective activity concentration parameters at each time point should recorded, not only as an indicator of the “quality” of the time-activity data but also because curve-fitting software often weight the data points by their respective standard deviations, fractional standard deviations, or other metrics of the statistical reliability of the data points.Organ-level dosimetry software typically requires input of the TIAC for source regions of a reference phantom. The phantom may represent the same species as the study subject(s) or a different species. Importantly, dosimetry estimates computed using a reference phantom involve extrapolation, that is, the biodistribution for the phantom is derived from the study subject(s) which differ in anatomy from the phantom.Several methods have been introduced for such extrapolations. The first-order approach prescribed by this Guide assumes that the body mass-normalized SUV is equivalent among species and phantoms used to approximate them:viz:The fraction of administered activity in the phantom source regions, Application of The hematopoietic (red) marrow is extremely radiosensitive and is commonly the dose-limiting tissue for therapeutic radiopharmaceuticals. It is difficult to harvest pure red marrow samples from the bones of small-animal subjects. For dosimetric purposes, it is commonly assumed that the activity concentration in the blood is representative of that of the red bone marrow; implicit in this is the assumption that the administered radiopharmaceutical does not localize specifically in or on any marrow component. This is typically a conservative assumption reasonable for translational dosimetry. Therefore, the protocol adopts this assumption and prescribes the following equation for computing the TIAC of phantom red marrow:The fraction of administered activity in the whole body can be used to determine the TIAC for the urinary bladder and the rest-of-body source regions. Due to differences in experimental design and measurement capabilities, we have provided several options for computation of the total body TIAC. If the animal total-body mean activity concentration is known, then the ex vivo measurements of the intact animal.Eqn. 12 is generally useful for deriving ex vivo counting experiments, then the partially sampled from the carcass:If mean activity concentration is estimated from animal carcass measurements, as is common is ex vivo biodistribution measurements where the activity concentrations are available for animal organs and remaining carcass, but the masses of the tissues are not.immediately post-radiopharmaceutical administration and record the activity reading ex vivo counting  counting vial. Another approach to assaying whole-body activity is as follows. Briefly place the anesthetized animal, in a plastic bag, in a dose calibrator ting see  below.At this point, we have estimated fractions of administered activity in the phantom source regions at discrete time points on a continuous time-activity curve, namely, In this variation, the time-activity curve is approximated as a piecewise linear function that passes through each measured point. The area under this function is then computed using the trapezoidal rule, wherein the area is divided into trapezoids with vertices defined by the measured points and their projections onto the time axis. The trapezoidal areas are then summed to determine the TIAC accumulated over the experimental measurement interval  parameter values are found. The general form of fitting functions used for radiopharmaceutical dosimetry is:20; the latter is outside the scope of this guide. Importantly, The total number of components of clearance, 1If the amplitude coefficients of the function in 21,NUKFIT20, and OLINDA/EXM. Other more general statistical software also may be used; these include SAAM-II22, Graph Pad Prism, and the Microsoft Excel Solver add-in.Several software tools are designed for performing exponential regression for radiopharmaceutical dosimetry, including MIRDfitFor source regions corresponding to major visceral organs, compute the TIAC using vide infra).The clearance parameters for the whole body can be used to estimate the TIAC for unique regions of the body, including the urinary bladder and the rest of body . An alternative to direct measurement of the urinary bladder TIAC has been demonstrated, which estimates the urinary bladder TIAC based on total body clearanceThe rest of body is a unique source region representing the collective tissues that have not been explicitly assigned a TIAC. The dose contribution from the rest-of-body TIAC can be estimated with dosimetry software (Step 5).The TIAC for the phantom rest of body, † for the source regions  Select radionuclide, 2) select anatomic phantom, 3) Enter TIACs regions . As a cror equivalent dose coefficients for each target organ and, 2) the effective dose coefficient.Following input of the TIACs, most software will immediately report: 1) the absorbed dose coefficients  for similar radiopharmaceuticals. If major discrepancies are identified, their source(s) should be investigated. Most software will generate an input echo to aid in identifying potentially mis-entered data or other blunders. Cross-validation may also be useful – namely, using alternative dosimetry models, TAC fitting approaches, or software tools to independently calculate the dosimetric quantities for comparison. One approach to checking dosimetry results is based on the reasonable assumption that the major dose contribution to a particular tissue is due to complete local absorption of particulate-radiations  emitted within the tissue. This tissue “self dose” may then be approximated as the product of the tissue’s TIAC per unit mass and the radionuclide’s mean energy emitted per decay in the form of such non-penetrating (np) radiations, Δnp, available in various tabulations of nuclear decay-scheme data. This estimate of each tissue’s absorbed dose coefficient and that reported by the dosimetry software should be in reasonable, though not exact, agreement.Naturally, every computation should undergo a “sanity” check to judge the reliability of the results. The results should be checked for consistency; that is, it should be verified that the dose coefficients are within the expected range based on previous studies or reference valuesA worked and annotated example of a human dosimetry estimate extrapolated from murine biodistribution data is provided in the electronic supplemental information.A basic protocol for preclinical dosimetry estimation is provided. It is intended to serve as a resource for deriving dosimetry estimates to support basic and translational radiopharmaceutical science. Although the concepts discussed can be applied to dosimetry in human research subjects or patients, the clinical application of these concepts should involve trained personnel, including a nuclear medicine physician and qualified medical physicist, as well as the use of approved software.


The present study examined the effectiveness of increasing levels of exposure therapy, which is applied for the treatment of maladaptive behaviors and anxiety. A total of 16 sessions were applied to the study group in the experimental group three times a week for 10 weeks. Patients aged ≥18 years whom the referring clinician evaluated as meeting the criteria for the Diagnostic and Statistical Manual of Mental Disorders, fourth edition (DSM-V-TR) Generalized Anxiety Disorder were included in the study. For the control group, demographic characteristics and Spielberger's State-Trait Anxiety Inventory were applied in the first session, followed by Spielberger's State-Trait Anxiety Inventory as a post-test and follow-up. Electroencephalography (EEG) recordings of the study group were obtained at the cortical level. Electrodes for EEG measurements were recorded using the International 10/20 Electrode Placement System. EEG data were obtained using the EEG Analysis Program software. Following the data collection phase, all data were entered into cells based on items using SPSS 25 software. When the findings obtained in the study were examined, it was determined that the increasing levels of exposure and behavioral therapy applied for maladaptive anxiety decreased the anxiety levels compared to those before therapy. This finding can be interpreted as that the cortical function-oriented application method for anxiety effectively reduced the anxiety levels of the study group. However, EEG asymmetry revealed a change in the data before and after the application. These findings demonstrate that the application affects the EEG asymmetry changes at the cortical level. The expansion of the prefrontal cortex (PFC) in the human brain is considered to be responsible for the subjective experience of anxiety and the ability to regulate anxiety-related responses ,2. WhileThe hippocampus, known for its role in memory formation, is also crucial in regulating emotions during fear conditioning . Unlike Understanding the role of the PFC in anxiety disorders has been challenging due to the complex nature of neural processes associated with anxiety. The PFC is responsible for assessing the likelihood of a threat in the environment by gathering information from different brain regions . DistortThe author initiated the data collection process after obtaining permission from the Ethics Committee of Sakarya University (registration no. 22.11.1122); written informed consent was obtained from all subjects. Subjects were under no obligation to participate in the study and were assured of the confidentiality of all information.https://quantifyinghealth.com).The present study was an experimental research study based on cause-and-effect relationships, using a pre-test and post-test control group design. Experimental studies examine the change caused by one or more dependent variables on an independent variable, providing accurate results using comparable methods. However, the present study was designed as a quasi-experimental model. The pre-test and post-test control group design is commonly employed in comparison studies conducted using experimental models. The present study specifically employed the pre-test post-test control group design   were incPrior to commencing the research, all necessary units of the private health institution were informed about the research and the process, and the necessary permissions were obtained. All persons, units and institutions participating in the process were informed, and their application and research permissions were obtained.At this stage, the participants in the study group were informed about the increasing levels of exposure therapy and cognitive behavioral therapy.After meeting with the client, a detailed conversation about anxiety, the treatment process for the client, and short and long-term treatment processes were determined. A form was prepared by discussing anxiety-related issues with each client and creating a list. Brain-based explanations for anxiety were given to each client. Short psychoeducational presentations were made for questions, such as how the brain works and what it needs. After the presentations, a form was created that included a list of clients who would participate in the exposure therapy and cognitive behavioral therapy. The goals selected from the list were divided into achievable tasks to gradually relieve the clients' anxiety. Behavioral changes were made by changing each client's behaviors towards different goals in this way and dividing them into small, easy practices. Clients were exposed to situations that aroused the sensation that they had difficulty in doing with increasing frequency, and the brain was reprogrammed. Any tasks that the clients could not carry out during the session were given to them as a home assignment. Unfulfilled home assignments were requested again, and support was provided for carrying out the home assignments. In this manner, the clients were provided with their comfort zones with measured and frequent steps, and the control of their home assignments was ensured. It was explained to the clients that moderate and reasonable anxiety strengthens memory. Thus, increasing levels of adrenaline in the brain play a role in encoding and reinforcing the implicit memory of the amygdala. This information enabled the clients to perform their home assignments meticulously. At the end of the application, the clients were informed that the research results would be shared and were thanked for their participation.Anxiety levels for the experimental group were measured using Spielberger's State-Trait Anxiety Inventory (pre-test and post-test) immediately before and after using the therapeutic method. After applying this therapeutic method, the anxiety levels were measured again. The demographic characteristics of the participants and Spielberger's State-Trait Anxiety Inventory were filled in the first session for the control group; the Spielberger's State-Trait Anxiety Inventory was then completed again. The measurement tools used are described below.This form included eight questions about sex, economic status, employment status, educational status and personal health.The scale measures normal and abnormal traits and state anxiety levels of individuals . There aElectrodes for EEG measurements were recorded using the International 10/20 Electrode Placement System. EEG data were visually scored for artifacts from blinking, eye movements and other motor movements when amplitudes exceeded ±50 V using the EEG Analysis Program software  All artifact-free EEG data were analyzed using a 1-second-wide discrete Fourier transform (DFT). Power (square microvolts) was derived from the DFT output in three alpha frequency bands .After the data collection phase was over, all data were entered into the cells on an item basis using the Statistical Program for Social Sciences 25 00 package program (IBM Corp.), and the total scores obtained from the scales were obtained.The data obtained from the personal information form were analyzed using the descriptive analysis method, and the frequency and percentage distributions of the sociodemographic information of the study group were obtained. It was examined whether the data obtained exhibited a significant difference before and after the therapeutic application in the experimental and control groups. The data collected in the experimental and control groups were analyzed using descriptive and inferential statistical tests, such as an independent t-test (to compare the average depression level in the two groups) and a paired t-test (to compare the average depression level) using the SPSS-25 program to determine the anxiety level before and after the intervention. Moreover, the Chi-squared test was used to investigate the demographic characteristics of the study participants. Participants' Spielberger's Trait-State Anxiety Inventory, pretest, posttest, and follow-up test scores were analyzed by ANOVA and ANCOVA and multiple comparisons were analyzed using Tukey's HSD test. Finally, reliability analyses were conducted for the reliability of the scale used in the study. The results were evaluated at 95% confidence intervals. A value of P<0.05 was considered to indicate a statistically significant difference.All the demographic characteristics of the study participants are presented in As shown in As shown in In addition, preliminary checks were made to confirm that the variances were not violated, reliable measurement of normality, linearity, homogeneity of variances, and homogeneity of regression trends. According to the results of ANCOVA, no significant difference was found between the post-test mean scores adjusted for Spielberger's State-Trait Anxiety Inventory according to sex (P>0.05) . In otheAs shown in The changes in the frontal and parietal lobe frequencies were examined. In the experimental group, the analysis was performed separately for the resting EEG asymmetry alpha right and left before and after the therapeutic application. It was determined that there was a significant interaction at 10-13 Hz for alpha right and left relative to the frontal region [t =1.344, PIn the present study, when the data obtained from the analyses were examined, the effectiveness of the gradually increasing levels of exposure therapy and cognitive behavioral therapy for maladaptive behavior and anxiety was examined. To date, to the best of our knowledge, there are no studies available in Turkey on the application of such methods, namely a brain-based psychological intervention program for anxiety. Therefore, the study is the first of its kind in Turkey. Herein, it was found that the methods used for maladaptive behavior and anxiety were effective and reduced the levels of anxiety in the study participants. This finding can be interpreted as an effective application method for anxiety.According to the follow-up evaluations at the end of the therapy, it was stated by all clients that they benefited greatly from the therapeutic application and that their quality of life increased compared to that before the therapy. A previous study on cognitive behavioral therapy demonstrated that the participants experienced a significant shift in their resting forebrain activity from greater relative right to greater relative left after receiving treatment . That stThe frontal EEG asymmetry-emotion model suggests that individuals with greater right frontal asymmetry exhibit higher anxiety symptoms . HoweverThe hippocampus has provided valuable insight into understanding the impact of stress on the brain. Research has expanded to include interconnected regions, such as the amygdala and PFC . In rodeA previous study discussed the association between reduced gray matter volume in the PFC and exposure to adverse events in humans. It also highlighted the impact of chronic stress on the functional connectivity and regulation of the PFC by the amygdala . AnotherIn line with the results obtained from the present study, further studies need to be conducted in Turkey, to further examine the effectiveness of increasing levels of exposure and behavioral therapy for maladaptive behavior and anxiety. It is also recommended that this therapy be used in clinics as a psychotherapy method and presented as behavioral homework. It is also recommended that brain-based methods be added as an additional protocol to all psychotherapy methods, applied and recommended for other psychological problems other than anxiety. It is recommended that the findings in the present study should be confirmed by supported other studies and repeated in future studies with different samples or study groups.


This study examined whether the behaviour of Internet search users obtained from Google Trends contributes to the forecasting of two Australian macroeconomic indicators: monthly unemployment rate and monthly number of short-term visitors. We assessed the performance of traditional time series linear regression (SARIMA) against a widely used machine learning technique (support vector regression) and a deep learning technique  in forecasting both indicators across different data settings. Our study focused on the out-of-sample forecasting performance of the SARIMA, SVR, and CNN models and forecasting the two Australian indicators. We adopted a multi-step approach to compare the performance of the models built over different forecasting horizons and assessed the impact of incorporating Google Trends data in the modelling process. Our approach supports a data-driven framework, which reduces the number of features prior to selecting the best-performing model. The experiments showed that incorporating Internet search data in the forecasting models improved the forecasting accuracy and that the results were dependent on the forecasting horizon, as well as the technique. To the best of our knowledge, this study is the first to assess the usefulness of Google search data in the context of these two economic variables. An extensive comparison of the performance of traditional and machine learning techniques on different data settings was conducted to enable the selection of an efficient model, including the forecasting technique, horizon, and modelling features. Forecasting the trends of economic indicators is crucial to policy makers and investors to make informed decisions. However, the official release of the indicators suffers from an information time lag because of the time and effort needed to collect the required data. To address this issue, researchers have aimed to nowcast and forecast the economic indicators.The unemployment rate is one of the key indicators due to its direct connection to the economic cycle and its influence on decision-makers. Several researchers have attempted to improve the forecasting for the unemployment rate for various developed and developing countries. While some authors have applied different machine learning techniques to forecast unemployment ,2, otherIn addition to the unemployment rate, we selected another indicator for our experiments, the number of short-term travellers visiting Australia. Being a destination for millions of tourists, the tourism industry in Australia is directly linked to its economic wellbeing. Forecasting the number of incoming travellers will assist investors in making their investment decisions and government agencies to properly allocate their resources to accommodate the number of travellers. Researchers have used online search data for different applications within the tourism industry. While some have focused on forecasting the hotel demand for particular cities or countries ,7,8, othThe selection of the two indicators analysed in this study, which are released monthly by the Australian Bureau of Statistics, was based on their ability to reflect the behaviour of Google users across different geographical locations. While Google Trends data collected within Australia were used to forecast the monthly unemployment rate, we employed globally searched keywords via the Google engine to forecast the number of travellers visiting Australia. This approach enabled us to assess the applicability of Google Trends data for two distinct settings and evaluate the forecasting horizon associated with the behaviours of both local and international users. Furthermore, we present a novel forecasting framework that selects the optimally performing model from two families of techniques suitable for forecasting time series data, namely traditional linear techniques (SARIMA and SARIMAX) and machine learning techniques (SVR). The framework also incorporates feature selection techniques, which play a crucial role in the forecasting process. It should be noted that prior literature had not extensively explored this aspect to the extent that is presented in this paper.In our paper, we examined the predictive power of Google Trends data using support vector regression (SVR) and convolutional neural networks (CNNs) against the traditional linear regression techniques such as SARIMA and SARIMAX in forecasting the two selected time series indicators. The paper is organised as follows. Over the last few years, several attempts have been made to explore the potential benefits of using Internet search data in forecasting economic variables . In thisForecasting unemployment has become an area of interest for researchers. There are two areas of focus to improve its accuracy: incorporating additional data sources (mainly Internet search data) and using non-traditional techniques.Incorporating online search data, in particular Google Trends, in unemployment forecasting has drawn researchers’ attention. Evidence can be found for research applied in different countries: the U.S. ,11,12,13These studies did not establish whether Internet data can replace or complement traditional methods. Some authors obtained better results when combining both data in their model . Most reThere is another set of research focused on using alternative techniques to forecast unemployment. Researchers have compared several machine learning techniques such as artificial neural networks (ANNs) ,30,31, SConsidering that researchers have not tested the impact of search data when forecasting unemployment using traditional and machine learning techniques, we were interested in assessing the efficacy of Google Trends in Australia where Google search is widely used. For this forecasting purpose, we employed SARIMA, SVR, and CNNs on an expanded list of search keywords that is related to Australia.The real-time characteristics of Internet search data have motivated researchers to examine their predictive power in the tourism and hospitality industry. The scope of past research varied from forecasting hotel demand to the number of visitors to cities and countries.Several research works have successfully employed Internet data to forecast the demand for hotel rooms and flights for different forecasting horizons ,7,8,32. While fewer studies have forecasted the number of visitors on a macro level, there has not been an assessment of the benefit of using search data with historical visitors’ data using machine learning techniques. In our paper, we used the same approach applied on unemployment data to evaluate the SARIMA and SVR results in forecasting the number of short-term visitors coming to Australia. A similar comparison was performed recently by Botta et al. , but insThe initial stage of our research involved data collection. We utilised two main sources of data: Australian economic indicators and Google Trends data. For the economic indicators, we extracted the historical data of two key indicators for the Australian economy from the Australian Bureau of Statistics’ website: monthly unemployment rate and monthly number of short-term visitors arriving in the country. These indicators represent essential aspects of the economy, and forecasting their future values would offer significant insights for policymakers and economic stakeholders. Those figures are often calculated by conducting surveys and collecting data from different agencies, leading to a delay in publishing the most-recent numbers. Monthly unemployment rate data are available from February 1978, while the number of visitors’ data cover the period starting in January 1991.Australia has a stable economy. The unemployment rate has not surpassed the 10% mark since 1994. Since then, the Australian unemployment rate has fluctuated between 4% and 6%. As seen in Australian unemployment data are seasonal in nature, where the same trend is repeated each year. For example, there has always been an increase in the unemployment rate post December, and this is expected to continue in the future. Since we used the SARIMA model, the parameter m that indicates the cycle of the trend was 12.A closer inspection of In parallel, we collected Google Trends data related to the aforementioned economic indicators. Google Trends data, which have been offered by Google since 2014, provide the search frequency of keywords, which shows the ratio of the search amount of a certain keyword to the total search amount of all keywords in a certain period of time, and then further normalises the search frequency into the interval of , which can avoid changes in the amount of keyword searches due to an increase in the number of users. It represents a rich source of insights about public interest in various topics over time. By selecting search terms related to the economic indicators, we could gauge public interest in these topics and examine the potential predictive power this interest holds for future economic conditions.In this paper, we searched for keywords related to each of the two target indicators used in this paper. For unemployment, the process of selecting search keywords began by considering what Internet users would search for if they became or were about to become unemployed . It seemThere were some limitations associated with selecting search keywords relevant to unemployment. Centerlink offers several services other than unemployment benefits; therefore, a change in its trend does not necessarily reflect the changes in demand for those benefits. Additionally, there are certain job vacancies relevant to industries such as construction that might not be posted on the “Seek” website. An increase in unemployment in the construction industry might not lead to an increase in access to the popular job search website. Furthermore, there are other popular platforms such as LinkedIn that can be accessed via a mobile application or directly through the website to look for job vacancies.Given the limitation of using Google Trends data, we intended to use the extracted time series data as a proxy for changes in the labour market, rather than an accurate reflection of changes in the Australian unemployment rate.The selected Google indicators to be used in forecasting the number of short-term visitors is shown in One of the limitations of using keywords looked up all over the world is that this includes the searches of users within Australia. Searches for those keywords by Australian residents do not contribute to the number of tourists visiting Australia. For this exercise, we assumed that the search for these terms within Australia did not create any noise as there were no noticeable changes in the search trends. Additionally, the search results were limited to the Google engine and did not include the usage of people residing in China due to the restriction on using Google in China. Chinese nationals consist of large proportion of tourists visiting Australia.After the data collection, we proceeded to the feature-engineering phase. The goal was to transform the collected data into a format that could be more effectively utilised by our predictive models. This involved creating new variables based on our raw data that better represent the underlying trend patterns for the predictive models. This process was applied in our study to increase the predictive performance of our models.For our dataset from the Australian Bureau of Statistics (ABS) and Google Trends, the original data were augmented by creating time-based features. These features were designed to capture the dynamic behaviour and trends in the data over time. These included lagged values of the indicators themselves and derived statistics such as moving averages.We created lag features for each dataset, specifically for the 12 previous months. The assumption here was that the current month’s value of a given economic indicator  or Google Trends value would have some correlation with its past values. For instance, if the unemployment rate was high last month, it could likely be high in the current month as well, barring any substantial changes in the economic environment.Lagged features were derived by shifting the time series data by one period (month) to create a new feature (Lag-1), by two periods to create another feature (Lag-2), and so on, up to twelve periods (Lag-12). This was carried out because it is plausible that both the dependent variables and the Google Trends indicators could have monthly seasonality that last up to a year, and we wanted our models to capture this potential seasonal effect.We also created moving average features, which represent the mean of the data points over a specified period. These were calculated for the last 3, 4,…, and 12 months. The rationale for creating these features is that, while individual data points (such as a spike in search interest or a dip in unemployment) can be quite volatile, the average value over a certain period can provide a smoother representation of the underlying trend in the data.In addition to the lag and moving average features, a “month” feature was created to capture any potential seasonal effects. This feature represents the month of the year (a number between 1 and 12) at each data point. This is particularly important for data such as tourism, which can show substantial variation depending on the time of year. The high-volatility components associated with time series data are often very difficult to model successfully; hence, a scaling and/or transformation process is usually performed on the series prior to implementing the actual experiments .Since we wished to be able to correctly predict the direction of movement of the number of short-term visitors, we applied a data transformation to the data series, which would result in better performance . Naturalty is the transformed number of visitors and tp is the original value.To achieve a logarithmic transformation with our short-term visitors’ data, the following equation was applied.In recent years, many feature-selection methods have been proposed. These methods can be categorised into three : filter,Filter methods calculate the score of each feature and rank them accordingly without dependency on the model. They are simple to implement, easy to interpret, and work effectively with high-dimensional data. Filter methods are fast strategies that provide good results in classification tasks ,40,41. AAfter engineering a wide range of features from the target variables and Google Trends indicators, we applied different feature-selection methods that incorporated recursive feature elimination (RFE) with mutual information (MI) and the f_test. These methods provided us with a robust and diverse perspective on feature importance. For the exogenous variables derived from Google Trends, we used the Pearson correlation to determine the most-relevant variables, which were used to train the SARIMAX model.The wrapper method, RFE, uses a machine learning algorithm  to rank features by importance and recursively eliminates the least-important features. This method can capture interactions between features since it uses a machine learning model for ranking.The filter methods, the f_test and mutual information, rank features based on their individual predictive power. The f_test checks the correlation between each feature and the target variable, while mutual information measures the dependency between the feature and the target. A higher mutual information means a higher dependency.By using these methods together, we obtained the benefits of both: the power of a machine learning model to capture complex relationships and the speed and simplicity of univariate statistics.The filter feature selection approach used for the SVR and CNN models is shown in Create a training dataset.Perform RFE using a decision tree as an estimator.Select the top 50% of the features from RFE.Compute the mutual information value (MIV) and f_test for the remaining features.Filter out the features based on the f_test and MIV. Select the top 10% of features based on the f_test and the top 25% based on the MIV.The approach of using the Pearson correlation as a feature-selection method for our SARIMAX model is a straightforward, yet effective one given that SARIMAX is not capable of modelling non-linear relationships.The Pearson correlation coefficient measures the linear relationship between two datasets. It ranges from −1 to 1. A correlation of −1 indicates a perfect negative linear relationship; a correlation of 1 indicates a perfect positive linear relationship; a correlation of 0 indicates no linear relationship.In our experiment, we selected only those exogenous variables that have a correlation value greater than 0.4 (either positive or negative) and considered to have a moderate to strong linear relationship with the dependent variable. This could help reduce the dimensionality of our data and might improve the interpretability and performance of our models.In summary, we chose a combination of feature selection and reduction techniques in our experiments to highlight the importance of incorporating such techniques in the modelling process to improve the accuracy of the models. The comparison of different techniques is out-of-scope for this paper. However, the selected techniques can detect different relationship between the created features and the target variable.The seasonal auto-regressive integrated moving average (SARIMA) is an extension of the ARIMA model. ARIMA models are a subset of linear regression models that attempt to use the past observations of the target variable to forecast future values. The “S” in SARIMA stands for seasonal. It adjusts the model to deal with repeated trends. Seasonal data can be easily identified by looking at repetitive spikes over the same period of time. Those spikes are consistently cyclical and easily predictable, which suggests that we should look past the cyclicality to adjust for it.Since SARIMA can only use the past values of Y and X, SARIMAX is used to incorporate exogenous variables. When using SARIMAX, the input data will include parallel time series variables that are used as a weighted input to the model.To find the optimal SARIMA and SARIMAX models, a grid search to determine the value of the parameters for the best model was performed. The best model found will have the lowest Akaike’s information criterion (AIC) and Bayesian information criterion (BIC).SARIMA and SARIMAX were used as the baseline models for the time series forecasting of the two Australian indicators of interest: monthly unemployment rate and monthly number of short-term visitors.Since the SARIMAX model can only detect the linearity between the target variable and the past values of the input data, we employed SVR and CNNs to check whether there was non-linearity between the input feature and the target variable, and therefore, the forecasting performance can be improved over that of SARIMAX.SVR, introduced by Drucker et al. , is a caConvolutional neural networks (CNNs) were introduced by Yann LeCun, Yoshua Bengio, and others in the 1990s . InitialTo carry out non-linear regression using SVR and CNN, it is necessary to create a higher-dimensional feature space from the time series data, as discussed in In order to evaluate the performance of the SARIMA, SVR, and CNN models on out-of-time sample data, we used two different metrics: mean-squared error (MSE) and symmetric mean absolute percentage error (SMAPE) . These tMSE is a metric corresponding to the expected value of the squared error or loss. If iŷ is the predicted value of the i-th sample and iy is the corresponding true value, then the MSE estimated over n (number of samples) is defined as:The SMAPE is an accuracy measure based on percentage (or relative) errors, defined as follows:At is the actual value and Ft is the forecast value.The At and Ft is divided by half the sum of the absolute values of the actual value At and the forecast value Ft. The value of this calculation is summed for every fit point t and divided again by the number of fit points n. A perfect SMAPE score is 0.0, and a higher score indicates a higher error rate.The absolute difference between Further statistical significance testing was applied to evaluate the performance of the different techniques and to determine if there were significant differences among them. One approach is to use the analysis of variance (ANOVA) on the predicted values generated by multiple models . ANOVA assesses the variation between the predicted values of different models and compares it to the overall variation in the data. The goal was to determine if there are statistically significant differences in the performance of the models.After performing ANOVA, if significant differences are detected, further analysis can be conducted using post hoc tests to identify specific pairs of models that significantly differ from each other. One commonly used post hoc test is Tukey’s honestly significant difference (HSD) test. The Tukey HSD compares all possible pairs of models and determines if the differences in their predicted values are statistically significant.The statistical significance approach helps with comparing and ranking the models based on their performance and identifying the models that significantly outperform or underperform others. It provides a quantitative and objective measure to assess the statistical differences between the techniques, allowing for informed decision-making in selecting the most-appropriate model for time series forecasting tasks.In this paper, we sought to examine the out-of-sample forecast performance of the SARIMA, SVR, and CNN models with a focus on two key Australian indicators: unemployment rate and monthly number of short-term visitors. The methodology, delineated in The design of our experiments was intended to assess the influence of the COVID-19 pandemic on the correlation between our chosen indicators and Google Trends data. By intentionally omitting data from the last three years and focusing on the pre-pandemic period, we evaluated if the dynamics between the indicators and Google Trends were dissimilar during a relatively more economically stable period.In each experimental setup, we constructed four iterations of each of our 12 models .In this section, we present an overview of the experiments’ results for each individual set of experiments. Additional comparison between Experiments 1 and 2 and Experiments 3 and 4 were conducted to highlight the difference in the performance between the models and the features selected for different data-driven settings influenced by COVID19. Given the large number of experiments and comprehensive statistical significance tests for the built models, only the comparison of results using the MSE are presented in Experiment 1:The first experiment revealed significant differences in performance among the models across the four forecasting horizons. The SARIMAX_ALL model outperformed all others for the 3-, 6-, and 12-month horizon levels, indicating its strong predictive power in the short- to mid-term. Interestingly, the SARIMA_HIST model, utilising historical data without the inclusion of exogenous variables, performed better for the 24-month horizon, hinting at its efficacy in capturing long-term trends and cycles.Compared to the SARIMA_RECENT, which takes into account only recent data, SARIMA_HIST’s superior performance for the 24-month horizon suggested that a broader historical context enhances long-term forecasting. SARIMAX_ALL’s outperformance of SARIMA_HIST and SARIMA_RECENT for shorter horizons demonstrated the value of integrating all available features, including exogenous variables, into time series models for short-term forecasts.Experiment 2:In the second experiment, the superiority of the SARIMAX_ALL model continued for the 6- and 12-month horizons, but faced competition from the CNN_TARGET_GI_FS model for the 3-month horizon. This indicates that deep learning models like CNN_TARGET_GI_FS can capture intricate data patterns more effectively in the short-term. For the 24-month horizon, however, the SARIMA_HIST model again outperformed, reaffirming the notion that simpler models utilising a broader historical context fare better in long-term forecasting.Feature selection models, such as SARIMAX_FS and CNN_TARGET_GI_FS, performed comparably to their all-feature counterparts for shorter horizons, suggesting that narrowing down the feature set does not necessarily impair short-term predictive capacity.Experiment 3:The third experiment introduced a new dominant model: SVR_TARGET_GI_FS. This machine learning model with feature selection demonstrated the best performance at the 3- and 6-month horizon levels, outperforming both SARIMA variants and SARIMAX_ALL. This suggested that machine learning techniques coupled with feature selection can excel in short-term forecasts. However, the SARIMAX_ALL model still held its ground for the 12-month horizon, and SARIMA_HIST regained superiority for the 24-month horizon.Again, feature selection models showed strong performance. The SVR_TARGET_GI_FS model’s superiority for shorter horizons over SARIMAX_ALL indicated that feature selection can even outperform all-feature models in certain situations.Experiment 4:In the final experiment, the deep learning model CNN_TARGET_GI_FS excelled for the 3- and 6-month horizons, while SARIMAX_ALL performed best for the 12-month horizon. For the 24-month horizon, the SVR_TARGET_FS model, a machine learning model with feature selection, surpassed other models, affirming the potency of feature selection for longer-term forecasting.Across all four experiments, the results demonstrated the strengths and weaknesses of each model for different forecasting horizons, the potential advantages of machine learning and deep learning techniques over traditional SARIMA/SARIMAX models, and the possible gains from employing feature selection.Taken together, these experiments provided nuanced insights into the interplay between traditional models (SARIMA and SARIMAX) and more modern, ML and DL techniques. While the former maintained strong performance at medium-term horizons, in particular when supplemented with a complete feature set, the latter—especially when utilising feature selection—appeared more-effective for both short- and long-term forecasting. Thus, the decision between ML/DL and traditional methods hinges on the forecasting horizon, underlining the importance of a targeted approach in time series prediction.Compared to SARIMA_RECENT, which takes into account only recent data, SARIMA_HIST’s superior performance for the 24-month horizon suggests that a broader historical context enhances long-term forecasting. SARIMAX_ALL’s outperformance of SARIMA_HIST and SARIMA_RECENT at shorter horizons demonstrated the value of integrating all available features, including exogenous variables, into time series models for short-term forecasts.Comparing both experiments, it was clear that the inclusion or exclusion of the COVID period data significantly influenced the predictive power of the models. In the shorter-term forecasts , the exclusion of the COVID period seemed to enhance the performance of models such as the CNNs, possibly due to the reduction of unprecedented volatility in the training data.In contrast, the SARIMAX model, which was the most-effective short- and mid-term forecasting model when the COVID data were included, saw its dominance reduced when the COVID data were excluded. This indicated that the SARIMAX model might be particularly effective at accounting for abrupt exogenous shocks such as the COVID pandemic.For the 24-month horizon, the SARIMA_HIST model remained the superior performer, with or without the COVID data, indicating its robustness in long-term forecasting regardless of drastic economic changes.These comparisons highlight the importance of considering the stability of the economic environment and the characteristics of the training data when selecting and interpreting forecasting models.Comparing both experiments, it became evident that the inclusion or exclusion of the COVID period data significantly impacted the models’ predictive performance. In the short-term forecasts , the exclusion of the COVID period data seemed to improve the performance of the CNN with the feature selection model, possibly due to the removal of the unpredictable COVID-induced volatility from the training data.Conversely, the SARIMAX using the all exogenous variables model, which was the most-effective short- and mid-term forecasting model with the COVID data included, saw a reduction in its dominance when the COVID data were excluded. This indicated that the model was particularly potent when dealing with abrupt exogenous shocks such as those experienced during the COVID-19 pandemic.For the long-term 24-month horizon forecast, the SARIMA_HIST model remained the best performer, irrespective of whether the COVID data were included or excluded, highlighting its robustness in long-term forecasting regardless of drastic changes in the economic environment.These findings underlined the importance of considering both the stability of the economic environment and the nature of the training data when choosing and interpreting forecasting models. They also demonstrated how different models may respond differently to periods of economic volatility, further emphasising the need for careful model selection based on the specific context and forecasting horizon.This research investigated the efficacy of various traditional and machine learning models in forecasting key economic indicators, namely the monthly unemployment rate and the monthly number of short-term visitors to Australia. It also explored the role of Google Trends data in enhancing the forecasting performance of these models.Overall, the results indicated that both machine learning (ML) and deep learning (DL) models offer considerable advantages over traditional SARIMA and SARIMAX models in forecasting these indicators, particularly in the shorter-term forecasting horizons. For instance, the SVR model demonstrated superior performance over SARIMA and SARIMAX in predicting the unemployment rate across all forecasting horizons in Experiments 1 and 2. Similarly, the CNN model was more effective than its traditional counterparts in predicting short-term visitor numbers in Experiments 3 and 4, especially in the short- to mid-term forecasting horizons.These findings align with the growing recognition of ML and DL techniques as valuable tools in economic forecasting, capable of handling complex data structures and identifying intricate patterns in the data. However, the results also underscored the robustness of traditional models such as SARIMA and SARIMAX in long-term forecasting, reminding us of their enduring relevance in certain forecasting contexts.Importantly, the inclusion of Google Trends data proved to enhance the forecasting performance of several models. Models incorporating Google Trends data, such as SARIMAX and the CNN with feature selection, consistently outperformed their counterparts that relied solely on historical data, particularly in the short- to mid-term forecasting horizons. These findings affirmed the potential of Google Trends data as a valuable supplement to traditional economic data, particularly in an era where digital information plays an increasingly central role in economic activities.This study, however, was not without its limitations. The forecasting performance of the models might be sensitive to the inclusion or exclusion of extreme events, such as the COVID-19 pandemic period data. The volatility introduced by such events can impact the predictive capability of different models in various ways, making it difficult to ascertain the most-effective model across all possible contexts.Furthermore, while the study considered a broad range of models and data types, there are still other potentially useful models and data sources that remain unexplored. For instance, other types of ML and DL models, such as recurrent neural networks (RNNs) and transformers, might offer different insights or outperform the models investigated in this study.Future research should aim to address these limitations and explore these uncharted territories. More-comprehensive investigations could consider a broader range of extreme events and their impacts on different models or investigate other types of ML and DL models and their efficacy in forecasting economic indicators. Moreover, future studies could explore other types of auxiliary data, such as social media data or other online data, to gauge their potential in enhancing economic forecasts.In conclusion, this research underscored the potential of ML and DL techniques in economic forecasting and highlighted the value of integrating Google Trends data into these models. However, it also stressed the importance of model selection based on the specific forecasting context and the need for the continuous exploration of novel models and data sources to enhance our forecasting capabilities.