Comparison Of Time Series Research Articles

A machine learning approach to fill gaps in dendrometer data

Abstract Key message The machine learning algorithm extreme gradient boosting can be employed to address the issue of long data gaps in individual trees, without the need for additional tree-growth data or climatic variables. Abstract The susceptibility of dendrometer devices to technical failures often makes time-series analyses challenging. Resulting data gaps decrease sample size and complicate time-series comparison and integration. Existing methods either focus on bridging smaller gaps, are dependent on data from other trees or rely on climate parameters. In this study, we test eight machine learning (ML) algorithms to fill gaps in dendrometer data of individual trees in urban and non-urban environments. Among these algorithms, extreme gradient boosting (XGB) demonstrates the best skill to bridge artificially created gaps throughout the growing seasons of individual trees. The individual tree models are suited to fill gaps up to 30 consecutive days and perform particularly well at the start and end of the growing season. The method is independent of climate input variables or dendrometer data from neighbouring trees. The varying limitations among existing approaches call for cross-comparison of multiple methods and visual control. Our findings indicate that ML is a valid approach to fill gaps in individual trees, which can be of particular importance in situations of limited inter-tree co-variance, such as in urban environments.

Conceptual model of the technology for calculating the similarity threshold of two audio sequences

The paper is focused on the pressing problem of speaker verification by means of voice time series comparison. The aim of this paper is to determine the orders of mel-frequency cepstral coefficients that most accurately describe the difference, between an authentic voice and an artificially generated copy for their further use as input to a neural network model in a resource-limited environment. To achieve this goal, the following tasks were accomplished: a conceptual model of the technology for determining the similarity threshold of two audio series was developed; the orders of fine-frequency cepstral coefficients with the most characteristic differences between the recording and the generated voice were determined on the basis of neural network analysis; an experimental study of the dependence of the execution time and computational load on the created feature vector when assessing the degree of similarity of two time series was conducted; and the optimal similarity threshold was determined on the basis of the chosen dataset. The developed model of the technology for determining the similarity threshold was tested on a dataset that is a combination of the DEEP-VOICE dataset and our own dataset. The demonstrated result of applying the developed technology showed an increase of 43% when using the specified MFCCs compared to using all of them. Based on experimental studies, the DTW acceptance threshold was set at 0.37.

Using cross-recurrence quantification analysis to compute similarity measures for time series of unequal length with applications to sleep stage analysis

Comparing time series of unequal length requires data processing procedures that may introduce biases. This article describes, validates, and applies Cross-Recurrence Quantification Analysis (CRQA) to detect and quantify correlation and coupling among time series of unequal length without prior data processing. We illustrate and validate this application using continuous and discrete data from a model system (study 1). Then we use the method to re-analyze the Sleep Heart Health Study (SHHS), a rare large dataset comprising detailed physiological sleep measurements acquired by in-home polysomnography. We investigate whether recurrence patterns of ultradian NREM/REM sleep cycles (USC) predict mortality (study 2). CRQA exhibits better performance compared with traditional approaches that require trimming, stretching or compression to bring two time series to the same length. Application to the SHHS indicates that recurrence patterns linked to stability of USCs are associated with all-cause mortality even after controlling for other sleep parameters, health, and sociodemographics. We suggest that CRQA is a useful tool for analyzing categorical time series, where the underlying structure of the data is unlikely to result in matching data points—such as ultradian sleep cycles.

Within-subject time series angular velocity differences between in-game high and low velocity fastballs in college baseball pitchers

PurposeThe purpose of the current study is to investigate the within-pitcher differences in time series angular velocities of the pelvis, trunk, shoulder, and elbow for high and low velocity fastballs in college baseball pitchers. MethodsIn-game data were retrospectively analyzed from 82 NCAA Division 1 pitchers ([1.89 ​± ​0.06] m, [92.8 ​± ​9.5] kg). Kinematic data were collected using an in-game markerless motion capture system. Time series data of pelvis, trunk, shoulder, and elbow angular velocities for each pitcher's fastest and slowest fastball were extracted for the pitch cycle (foot contact to ball release) and used for analysis. Within-subject time series comparisons were conducted using statistical parametric mapping (SPM) paired samples t-tests (α ​= ​0.012 5). ResultsEach of the tested segments were significantly faster in the fastest fastball trial compared to the slowest fastball trial. The duration of significance in reference to the pitch cycle, test statistic, and p-value, for each segment are as follows: Pelvis: 0%–4%, t ​= ​3.54, p ​= ​0.012; Trunk: 30%–67%, t ​= ​5.62, p ​< ​0.001; Shoulder External Rotation: 3%–50%, t ​= ​−6.03, p ​< ​0.001; Shoulder Internal Rotation: 96%–100%, t ​= ​4.11, p ​= ​0.008; Elbow: 75%–86%, t ​= ​4.13, p ​< ​0.001. DiscussionWithin-subjects differences exist in time series angular velocities when comparing the fastest and slowest fastball. These time series differences provide additional information to distinguish fastball velocity beyond what discrete metrics can provide. Pitchers should look to rotate each segment faster, and optimize the sequencing of these movements, to increase pitch velocity.

Comparative time series analysis of Anatolian water buffalo stock in Türkiye

Water buffalo holds an important place in the livestock heritage in Türkiye. In the current study, buffalo numbers between 2023 and 2032 were estimated by using buffalo number data from 1991 to 2022. In the study, FAOSTAT data between 1961 and 2021 and TÜİK data for 2022 were used to obtain the time series. ARIMA modeling method was used in the study conducted in R programming language. ARIMA is a time series model that can make predictions from time series based on explaining univariate data. According to the results of the analysis made in the study, it is seen that the number of buffaloes in Türkiye will continue to decrease. According to the results obtained, it is estimated that the number of buffaloes will be 157,755 heads in 2023, 96,851 heads in 2027 and 19,136 heads in 2032. The disease resistance of buffaloes, their high adaptability, the high demand for water buffalo products, the preference for high-yielding cows for milk production despite government support payments, increasing mechanization, the reduction of buffalo habitats and the increase in input costs have led to a decline in Anatolian water buffalo populations. To prevent the Anatolian water buffalo from being threatened with extinction, the population decline must be halted and improved. To ensure this, the decline of the pastures that form the buffalo’s habitat must be halted, pasture areas must be increased, and existing pastures rehabilitated, government subsidies for buffalo and calf rearing must be increased and market opportunities for buffalo products must be expanded.

Scalable Methods for Multiple Time Series Comparison in Second Order Dynamics

Statistical comparison of multiple time series in their underlying frequency patterns has many real applications. However, existing methods are only applicable to a small number of mutually independent time series, and empirical results for dependent time series are only limited to comparing two time series. We propose scalable methods based on a new algorithm that enables us to compare the spectral density of a large number of time series. The new algorithm helps us efficiently obtain all pairwise feature differences in frequency patterns between M time series, which plays an essential role in our methods. When all M time series are independent of each other, we derive the joint asymptotic distribution of their pairwise feature differences. The asymptotic dependence structure between the feature differences motivates our proposed test for multiple mutually independent time series. We then adapt this test to the case of multiple dependent time series by partially accounting for the underlying dependence structure. Additionally, we introduce a global test to further enhance the approach. To examine the finite sample performance of our proposed methods, we conduct simulation studies. The new approaches demonstrate the ability to compare a large number of time series, whether independent or dependent, while exhibiting competitive power. Finally, we apply our methods to compare multiple mechanical vibrational time series.

Delirium event and associated treatment modifications among older adults with Alzheimer's disease: An interrupted time-series analysis of Medicare data.

Both Alzheimer's disease (AD) and deliriogenic medications increase the risk of delirium in older adults. This study examined the association between delirium and the subsequent monthly use of anticholinergic, sedative, and opioid medications in the 1 year after delirium in older adults with AD. This comparative interrupted time series analysis involved adults (aged 65 years and older) with a diagnosis of AD initiating on cholinesterase inhibitors (ChEIs) based on 2013-2017 Medicare data. Separate patient-level segmented regression models were used for each outcome to evaluate changes in the cumulative anticholinergic burden (CAB), sedative load, and opioid load after the delirium/index event using a 12-month baseline and follow-up period among patients who had a delirium event and those without delirium (control group). Propensity score-based stabilized weights were utilized to balance baseline factors in the delirium and control groups. The study included 80,019 older adults with AD with incident ChEI use; 17.11% had delirium. There was an immediate decline in monthly CAB after the delirium event (mean estimate -0.86, p-value: 0.01) compared to the control group. A similar decline was observed when examining the sedative load (-0.06, p-value: 0.002) after the delirium event. However, there was no decline in opioid load (-0.50, p-value: 0.18). In the long term, CAB (0.13; p-value: <0.0001), sedative load (0.01; p-value: <0.001), and opioid load (0.07; p-value: 0.006) increased over the 1-year post-delirium period in the delirium group compared to those without delirium. This study found the burden of deliriogenic medications over the 1-year follow-up showed increasing trends in older adults with AD, even though there was some level shift in CAB and sedative load after the delirium event.

Synthesis of satellite and ground data provide unique perspectives for discovering the air pollution patterns: A case study in Guangdong Province, China

Existing studies have analyzed the spatio-temporal patterns of air pollutants by combining ground and satellite measurements, primarily for cross-validation purposes. However, the unique characteristics and discrepancies between satellite and ground measurements have rarely been leveraged to understand pollution patterns and identify air pollution sources. To our best knowledge, this study is the first to utilize these discrepancies to holistically analyze the spatial and temporal patterns and investigate local biomass-burning effects on the five typical air pollutants: particulate matter (PM2.5)/aerosol optical depth (AOD), carbon monoxide (CO), nitrogen dioxide (NO2), sulphur dioxide (SO2), and ozone (O3). Guangdong (GD) province was selected as a case study due to its complex air pollution sources and patterns. Ground-based analysis from 2015 to 2023 shows significant decreases in PM2.5, CO, NO2, and SO2, and a significant increase in O3 in urban areas, indicating the efficacy of stringent air pollution control policies. However, satellite analysis shows significant downtrend only in AOD, while the trends of other pollutants are almost negligible, which are likely to be evidence of industrial migration. Both measurements exhibit regular seasonal patterns for all air pollutants. In-depth time-series comparisons between ground and satellite data reveal seasonal consistency for NO2 but noticeable discrepancies for both AOD and CO, which could be attributed to urban-rural differences and local versus transported pollution sources. Spatially, AOD and NO2 exhibits the most significant regional discrepancies, followed by SO2 and CO, with higher values observed over Pearl River Delta (PRD) compared to non-PRD regions. O3 is more evenly distributed, showing more pronounced seasonal variations than regional differences. The synergetic use of satellite and ground measurements collectively verifies the significant local biomass-burning effects on the five pollutants. These findings can aid in developing more targeted air pollution control policies.

ARIMAX-Threshold 모형을 이용한 20대 이하 마약류 사범 검거 수 시계열 분석

In recent years, the number of drug offenders under 20s has surged, accounting for approximately 35.5% of all drug offenders in 2023, which becomes a serious social issue in Korea. The purpose of this work is to study and compare time series models for statistical analysis and prediction for the number of drug offenders under 20s. ARIMA and ARIMAX model is applied to the data of the number of drug offenders arrested under 20s. In order to further improve the predictability, a model added by threshold, reflecting the presence or absence of the exogenous variable, is proposed and compared. As for the exogenous variable, dark web data that is directly related to the number of drug offenders arrested, as a main drug dealer, is used. Based on cross-correlation coefficient analysis, the ARIMAX-Threshold model including indicator variables and threshold is proposed. Out-of-sample forecasting analysis is performed to compare the forecasting performance, and it is revealed that the ARIMAX-Threshold model proposed in this study improves the forecasting errors by up to 9.4%. The predicted values and prediction intervals of the data on the number of drug offenders under 20s until April 2025 are presented, which will contribute to help in policy development for drug crime prevention.

Forecasting of Monthly Crude Oil Prices in Kenya Using Comparative Time Series Models

Crude oil is one of the most vital products that ever existed and variation in prices affects all sectors of the economy and variation in its prices is very crucial. Therefore, without an accurate and appropriate predictive model for crude oil prices, it has proven difficult to predict future oil prices. Therefore, appropriate modeling is crucial for the oil companies to adjust strategies used in the production and supply as well as structural optimization. This study sought to fit several time series forecasting models namely; ARIMA, Naïve, Seasonal Naïve, Time Series Linear Model (TSLM), and Exponential Smoothing (ETS) to model and forecast crude oil prices. The study used Kenya’s monthly crude oil prices from Jan 2003 to Dec 2023, giving a sample of 252 observations. The selection of the best model was based on the minimization of the information criteria, where ARIMA, ETS, and Seasonal Naïve attained an AIC of 1294.193, 1846.780, and 1403.821, respectively. Similarly, the models attained the BIC of 1304.991, 1863.071, and 1450.489, respectively. Since the Naïve and TSLM could not provide the AIC and BIC, model selection was entirely based on the forecast accuracy measures. From the results, the Naive model reported the lowest RMSE (19.6329), indicating that it has the smallest average squared error, with the lowest MAE (15.5212), suggesting it has the smallest average absolute error. Besides, the Naive model reported an ME (1.9819) which is relatively low but not the lowest. The automatic ETS model has a slightly lower ME (3.478211). The naive model reported lower MPE and MAPE values (-3.9525 and 26.8022, respectively) compared to most models, indicating less percentage error. Similarly, a lower MASE and RMSSE were reported by the naïve model, (0.7343624) and RMSSE (0.7228792), respectively, indicating that the model performs well relative to forecasting crude oil prices in Kenya. The naïve model demonstrated a higher consistency and reliability in forecasting crude oil prices in Kenya.

Medications for Opioid Use Disorder after Entering Residential Treatment: Evidence from Louisiana Medicaid.

Policies have attempted to increase the use of medication for opioid use disorder (MOUD) during an admission to a residential treatment program, but little is known about the association of residential admission with subsequent MOUD use. In a cohort study of Louisiana Medicaid beneficiaries age 18-64 with diagnosed opioid use disorder (OUD), weekly MOUD use and overdose for 20 weeks before and after an admission to residential treatment was analyzed using comparative interrupted time series regression. Participants with residential treatment admission between January 1, 2018, and December 31, 2020 (N = 12,222) were compared against a demographically similar group of people with OUD without residential treatment during the study period. The samples with residential treatment were largely male (61.9%), White (47.2%), and aged 30 to 39 years (41.4%). At baseline, people admitted to residential treatment were much less likely to use MOUD than the comparison group (4.2% lower, CI: 3.8%, 4.5%, P < 0.01). After admission, use of any MOUD initially increased by 3.1% (P < 0.01) relative to the comparison group, which reverted to the counterfactual trend by 20 weeks. Post-admission MOUD use differed widely by medication. Overdose incidence was highest in the weeks right before admission, but otherwise, it did not change during the study period. Admission to residential treatment for OUD was associated with a temporary increase in MOUD use. Policy initiatives should focus on both boosting use of MOUD during residential treatment and sustaining access to MOUD in outpatient care in the weeks following discharge.

Estimating the effect of sand-roughened bed on hydraulic jump characteristics using heuristic models

The hydraulic jump occurs in open channels and downstream of hydraulic structures because these features change the flow regime from super-critical to sub-critical. To prevent downstream channel erosion and guarantee the construction of a hydraulic jump, a stilling basin is utilized. The effect of sand-roughened beds on hydraulic jump characteristics was investigated using an experimental study. After that, new machine learning models including Emotional neural network (EANN), Hammerstein Weiner model (HWM), Elman neural networks ENN, and Extreme learning neural networks (ELNN) were adopted to estimate the ratio of hydraulic jump length to initial water depth. Different evaluation criteria such as determination Coefficient (R2), Mean Square Error (MSE), Correlation Coefficient (R), and Rout Mean Square Error (RMSE), scatter plots, time series comparison, and Spiral plots have been used to evaluate the models' performance. The results revealed that the Elman NN model outperformed the other models in estimating the ratio of hydraulic jump length to the initial depth (Lj/y1), while the HWM model has a weaker performance than other models in estimating Lj/y1.

Relative Homogenization of Climatic Time Series

Homogenization of the time series of observed climatic data aims to remove non-climatic biases caused by technical changes during the history of the climate observations. The spatial redundancy of climate information helps to recognize station-specific inhomogeneities with statistical methods, but the correct detection and removal of inhomogeneity biases is generally not easy for the combined effects of individual inhomogeneities. In a homogenization procedure, several time series of a given climatic variable observed in one climatic region are usually homogenized together via a large number of spatial comparisons between them. Such procedures are called relative homogenization. A relative homogenization procedure may include one or more homogenization cycles where a cycle includes the steps of time series comparison, inhomogeneity detection and corrections for inhomogeneities, and they may include other steps like the filtering of outlier values or spatial interpolations for infilling data gaps. Relative homogenization methods differ according to the number and content of the individual homogenization cycles, the procedure for the time series comparisons, the statistical inhomogeneity detection method, the way of the inhomogeneity bias removal, among other specifics. Efficient homogenization needs the use of tested statistical methods to be included in partly or fully automated homogenization procedures. Due to the large number and high variety of homogenization experiments fulfilled in the Spanish MULTITEST project (2015–2017), its method comparison test results are still the most informative about the efficiencies of homogenization methods in use. This study presents a brief review of the advances in relative homogenization, recalls some key results of the MULTITEST project, and analyzes some theoretical aspects of successful homogenization.

Assessment of export-embodied CO2 emissions from China’s ocean industries: implications for formulating sustainable ocean policies

The ocean industries are characterized by being export-driven. The exports of ocean industries (hereafter termed ocean exports) caused environmental pollution with amounts of CO2 emissions and thereby affected climate change. There is a need, therefore, for accurate assessments of CO2 emissions embodied in ocean exports—which can help policymakers adopt targeted emission-reduction measures to formulate sustainable ocean policies. However, few studies of ocean-industry emissions considered impacts in sectoral and trade pattern heterogeneity, especially from export perspective. To fill this gap, we measured and evaluated the export-embodied CO2 emissions from China’s ocean industries, based on our newly developed high-resolution and comparable time-series environmentally extended input–output database, called EE-DPN-OEIOT. The results showed that China’s ocean exports generated 94.3 Mt of embodied CO2 emissions in 2017, with nearly 40% originating from processing ocean exports. Regarding the evolution from 2007 to 2017, the total export-embodied CO2 emissions from ocean industries decreased by 7.3%, while the embodied CO2 emissions in processing ocean exports increased by 50.1%. From 2007 to 2017, the decrease in carbon emission intensity was the major driving factor of the downturn in export-embodied CO2 emissions across the total ocean economy and for seven ocean subsectors (60%), while the export-scale effect primarily drove the increases in CO2 emissions. Moreover, there were disparities in the driving factors behind changes in embodied CO2 emissions between processing and non-processing ocean exports. Based on our findings, we proposed three recommendations from a trade perspective to facilitate low-carbon sustainable transition of China’s ocean economy, thus better fulfilling Sustainable Development Goal 14.

A time series analysis and comparison of predictive models for the demand for healthcare equipments

A time series analysis and comparison of predictive models for the demand for healthcare equipments

Comparative time-series multi-omics analyses suggest H1.2 involvement in anoxic adaptation and cancer resistance.

The naked mole rat (NMR), Heterocephalus glaber, is known as the longest-lived rodent and is extraordinarily resistant to hypoxia and cancer. Here, both NMR embryonic fibroblasts (NEFs) and their mouse counterparts (MEFs) were subjected to anoxic conditions (0% O2, 5% CO2). A combination of comparative transcriptomics and proteomics was then employed to identify differentially expressed genes (DEGs). Notably, we observed distinct levels of histone H1.2 (encoded by HIST1H1C) accumulation between NEFs and MEFs. Subsequent mechanistic analyses showed that higher H1.2 expression in NEFs was associated with the lower expression of its inhibitor, PARP1. Additionally, we discovered that H1.2 can directly interact with HIF-1α PAS domains, thereby promoting the expression of HIF-1α through facilitating the dimerization with HIF-1β. The overexpression of H1.2 was also found to trigger autophagy and to suppress the migration of cancer cells, as well as the formation of xenograft tumors, via the NRF2/P62 signaling pathway. Moreover, an engineered H1.2 knock-in mouse model exhibited significantly extended survival in hypoxic conditions (4% O2) and showed a reduced rate of tumor formation. Collectively, our results indicate a potential mechanistic link between H1.2 and the dual phenomena of anoxic adaptation and cancer resistance.

A method for comparing time series by untangling time-dependent and independent variations in biological processes

A method for comparing time series by untangling time-dependent and independent variations in biological processes

Time series clustering using fragmented autocorrelations

We propose and study an autocorrelation procedure designed to characterize and compare large sets of long time series. This time-domain procedure is contrasted with a frequency-domain approach that has recently been introduced and discussed in the literature. In both cases, instead of using all the information available from data, which would be computationally very expensive, adequate regularization rules select and summarize the most relevant information suitable for clustering purposes. Essentially, we suggest to use the autocorrelation coefficients of the time series that are only computed around the lags of greatest interest. Then, we study this method in several ways. We argue theoretically that fragmenting the autocorrelation function can have efficiency advantages when comparing time series. By means of a large simulation study, we show that the suggested procedure can condense the relevant information of the time series. We compare its results with those from the frequency domain counterpart. We further illustrate this procedure in a study of the evolution of several stock markets indices and show the effect of recent financial crises on the behaviour of these indices.

Mapping rice-crayfish co-culture (RCC) fields with Sentinel-1 and -2 time series in China's primary crayfish production region Jianghan Plain

Crayfish is a high-risk invasive species with devastating impacts on freshwater ecosystems. Meanwhile, nicknamed “little lobster”, it is a popular food in many countries including China. The crayfish production in China increased from 1.13 to 2.39 million tons in 2017–2020, accounting for 97% global production. This phenomenal increase is attributed to the expansion of the rice-crayfish co-culture (RCC) farming mode whose area increased by 123% from 0.57 to 1.26 million ha in 2017–2020. However, the fast expansion of RCC is undertaken in an uncontrolled and unregulated manner, referred by some researchers as a “blind expansion”. It raises wide concerns on ecological risks (crayfish can escape in high-magnitude floods), endangerment of riverbanks (crayfish burrows), food security (reduced rice production), excessive water consumption, and greenhouse gas (methane) emission. It is thus urgent to accurately map the spatial distributions of RCC fields using satellite remote sensing data, so as to assess the ecological and environmental impacts and risks, and to better regulate the expansion. However, there are currently no practically-scalable approaches to reliably map RCC fields in large areas. In particular, there lack the knowledge on the relationship between satellite observations and on-ground biophysical processes in RCC fields. In this study, we conducted field surveys in RCC fields, and in particular, the daily water levels in RCC fields were measured for the complete year of 2020. The comparison of annual water-level time series and satellite-NDVI time series, combined with the RCC farming information collected in surveys, reveals how satellite observations vary in correspondences to on-ground biophysical processes in RCC fields; and importantly, it provides information on how RCC fields can be efficiently distinguished from other land covers using satellite data. Based on that, we propose an approach to map RCC fields from annual Sentinel-2 optical-wavelength and Sentinel-1 Synthetic Aperture Radar (SAR) time series, utilizing the annual water-occurrence frequency (AWF) and characteristic phenological features derived from the satellite data. This method was demonstrated in Jianghan Plain, the primary crayfish production region in China with an area of approximately 37,000 km2. A total of 273,365 ha (2733.65 km2) RCC field area in year 2020 was mapped, which accounted for 24.6% of the whole plain's cropland area (approximately 11,100 km2), meaning a significant proportion of the rice paddies were converted to RCC fields. The RCC mapping accuracies were validated using the samples collected in field surveys and also from Google Earth images, and was compared with the state-of-practice RCC mapping method using bi-seasonal optical-wavelength satellite images. The proposed method obtained 93.8% overall accuracy and 0.91 kappa coefficient, and outperformed the compared bi-seasonal method. The proposed method is scalable for large-area and multi-annual applications. Future research regarding improvements and applications is recommended.

A causal machine-learning framework for studying policy impact on air pollution: A case-study in COVID-19 lockdowns.

When studying the impact of policy interventions or natural experiments on air pollution, such as new environmental policies and opening or closing an industrial facility, careful statistical analysis is needed to separate causal changes from other confounding factors. Using COVID-19 lockdowns as a case-study, we present a comprehensive framework for estimating and validating causal changes from such perturbations. We propose using flexible machine learning-based comparative interrupted time series (CITS) models for estimating such a causal effect. We outline the assumptions required to identify causal effects, showing that many common methods rely on strong assumptions that are relaxed by machine learning models. For empirical validation, we also propose a simple diagnostic criterion, guarding against false effects in baseline years when there was no intervention. The framework is applied to study the impact of COVID-19 lockdowns on NO2 in the eastern US. The machine learning approaches guard against false effects better than common methods and suggest decreases in NO2 in Boston, New York City, Baltimore, and Washington D.C. The study showcases the importance of our validation framework in selecting a suitable method and the utility of a machine learning based CITS model for studying causal changes in air pollution time series.