Autoregressive Time Series Models Research Articles

Forecasting multidimensional autoregressive time series model with symmetric $$\alpha$$-stable noise using artificial neural networks

Forecasting multidimensional autoregressive time series model with symmetric $$\alpha$$-stable noise using artificial neural networks

Combining wavelet-enhanced feature selection and deep learning techniques for multi-step forecasting of urban water demand

Abstract Urban water demand (UWD) forecasting is essential for water supply network optimization and management, both in business-as-usual scenarios, as well as under external climate and socio-economic stressors. Different machine learning and deep learning models have shown promising forecasting skills in various areas of application. However, their potential to forecast multi-step ahead UWD has not been fully explored. Modelling uncertain UWD patterns and accounting for variations in water demand behaviors require techniques that can extract time-varying information and multi-scale changes. In this research, we comparatively investigate different state-of-the-art machine learning- and deep learning-based predictive models on 1-day- and 7-day-ahead UWD forecasting, using daily demand data from the city of Milan, Italy. The contribution of this paper is two-fold. First, we compare the forecasting performance of different machine learning and deep learning models on single- and multi-step daily UWD forecasting. These models include Artificial Neural Network (ANN), Support Vector Regression (SVR), Light Gradient Boosting Machine (LightGBM), and Long Short-Term Memory network with and without an attention mechanism (LSTM and AM-LSTM). We benchmark their prediction accuracy against autoregressive time series models. Second, we investigate the potential enhancement in predictive accuracy by incorporating the wavelet transform and feature selection performed by LightGBM into these models. Results show that, overall, wavelet-enhanced feature selection improves the model predictive performance. The hybrid model combining wavelet-enhanced feature selection via LightGBM with LSTM (WT-LightGBM-(AM)-LSTM) can achieve high levels of accuracy with Nash-Sutcliffe Efficiency larger than 0.95 and Kling–Gupta Efficiency higher than 0.93 for both 1-day- and 7-day-ahead UWD forecasts. Furthermore, performance is shown to be robust under the influence of external stressors causing sudden changes in UWD.

Statistical Models for Outbreak Detection of Measles in North Cotabato, Philippines

A measles outbreak occurs when the number of cases of measles in the population exceeds the typical level. Outbreaks that are not detected and managed early can increase mortality and morbidity and incur costs from activities responding to these events. The number of measles cases in the Province of North Cotabato, Philippines, was used in this study. Weekly reported cases of measles from January 2016 to December 2021 were provided by the Epidemiology and Surveillance Unit of the North Cotabato Provincial Health Office. Several integer-valued autoregressive (INAR) time series models were used to explore the possibility of detecting and identifying measles outbreaks in the province along with the classical ARIMA model. These models were evaluated based on goodness of fit, measles outbreak detection accuracy, and timeliness. The results of this study confirmed that INAR models have the conceptual advantage over ARIMA since the latter produces non-integer forecasts, which are not realistic for count data such as measles cases. Among the INAR models, the ZINGINAR (1) model was recommended for having a good model fit and timely and accurate detection of outbreaks. Furthermore, policymakers and decision-makers from relevant government agencies can use the ZINGINAR (1) model to improve disease surveillance and implement preventive measures against contagious diseases beforehand.

Bayesian quantile inference and order shrinkage for hysteretic quantile autoregressive models

Hysteretic quantile autoregressive model combines the hysteretic patterns and quantile autoregression, which can capture the dynamic relationship and nonlinear characteristics at different quantiles in time series data. In this paper, the Bayesian quantile inference and order shrinkage are studied for a class of hysteretic quantile autoregressive time series models. By using Markov Chain Monte Carlo (MCMC) techniques, the proposed Bayesian quantile method can handle the sparse hysteretic quantile autoregressive model well. It can accurately determine order of the model and estimate non-zero coefficients. Both simulation studies and a data example show that the proposed methods are feasible, reliable and appropriate for analysing the US Gross National Product data set.

A class of kth‐order dependence‐driven random coefficient mixed thinning integer‐valued autoregressive process to analyse epileptic seizure data and COVID‐19 data

SummaryData related to the counting of elements of variable character are frequently encountered in time series studies. This paper brings forward a new class of th‐order dependence‐driven random coefficient mixed thinning integer‐valued autoregressive time series model (DDRCMTINAR()) to deal with such data. Stationarity and ergodicity properties of the proposed model are derived in detail. The unknown parameters are estimated by conditional least squares, and modified quasi‐likelihood and asymptotic normality of the obtained parameter estimators is established. The performances of the adopted estimate methods are checked via simulations, which present that modified quasi‐likelihood estimators perform better than the conditional least squares considering the proportion of within‐ estimates in certain regions of the parameter space. The validity and practical utility of the model are investigated by epileptic seizure data and COVID‐19 data of suspected cases in China.

Uncovering the relationship between incidental emotion toward a disaster and stock market fluctuations: Evidence from the US market

Despite having potentially important implications, there has been little research on the relationship between the public's incidental emotion and the stock market. To that end, we construct a valence-based measure of incidental emotion using BERTweet's sentiment analysis and empirically investigate the association between collective incidental emotion toward the COVID-19 pandemic and the U.S. stock market. We employ multivariate time series autoregressive models to test the relationship between emotion polarity and stock market returns or trading volumes. The results reveal that societal sentiment toward the pandemic has a significant effect on the returns of the Dow Jones Industrial Average and S&P 500. In contrast, the macro-level emotion does not significantly affect the return for NASDAQ 100. The findings also suggest a significant association between incidental emotion and trading volumes. We conduct a battery of sensitivity tests that further support our conjecture. The study underscores the robust role of incidental emotion in investment decision-making, highlighting its significance as a distinctive feature that should be incorporated into financial decision support systems.

Gibbs sampler for Bayesian prediction of triple seasonal autoregressive processes

Researchers have extended autoregressive (AR) time-series models to adequately fit and model time-series with triple seasonality. These AR extensions can be referred to as triple seasonal AR (TSAR) models. For these TSAR time-series models, only Bayesian estimation and identification have been introduced. Therefore, in this article, we aim to extend the existing work for presenting the Bayesian prediction for TSAR models using the Gibbs sampler algorithm. In this Bayesian prediction, we first assume the TSAR errors are identically normally distributed, and we employ normal-gamma and g priors for the TSAR parameters. Based on the normally distributed TSAR errors and the specified TSAR parameters’ priors, we are able to derive the conditional predictive and posterior densities. Particularly, we show the conditional posterior densities of TSAR coefficients and variance are the multivariate normal and inverse-gamma, respectively. In addition, for the future TSAR observations, we show the conditional predictive density is the multivariate normal. Using these derived full conditional distributions, we propose the Gibbs sampler to efficiently approximate the joint predictive and posterior densities and to easily carry out multiple-step ahead predictions. We validate the accuracy of forecasting for the proposed Gibbs sampler by conducting a simulation study. Moreover, we apply the proposed Gibbs sampler to hourly electricity-load time-series datasets in some European countries, along with a comparison with the well-known long-short term memory (LSTM) recurrent neural model.

Spatio-temporal epidemiology of Japanese encephalitis virus infection in pig populations of eastern Uttar Pradesh, India, 2013-2022.

Japanese encephalitis (JE) is endemic in India. Although pigs are considered important hosts and sentinels for JE outbreaks in people, limited information is available on JE virus (JEV) surveillance in pigs. We investigated the spatio-temporal distribution of JEV seroprevalence and its association with climate variables in 4451 samples from pigs in 10 districts of eastern Uttar Pradesh, India, over 10 years from 2013 to 2022. The mean seroprevalence of IgG (2013-2022) and IgM (2017-2022) was 14% (95% CI 12.8-15.2) and 10.98% (95% CI 9.8-12.2), respectively. Throughout the region, higher seroprevalence from 2013 to 2017 was observed and was highly variable with no predictable spatio-temporal pattern between districts. Seroprevalence of up to 60.8% in Sant Kabir Nagar in 2016 and 69.5% in Gorakhpur district in 2017 for IgG and IgM was observed, respectively. IgG seroprevalence did not increase with age. Monthly time-series decomposition of IgG and IgM seroprevalence demonstrated annual cyclicity (3-4 peaks) with seasonality (higher, broader peaks in the summer and monsoon periods). However, most variance was due to the overall trend and the random components of the time series. Autoregressive time-series modelling of pigs sampled from Gorakhpur was insufficiently predictive for forecasting; however, an inverse association between humidity (but not rainfall or temperature) was observed. Detection patterns confirm seasonal epidemic periods within year-round endemicity in pigs in eastern Uttar Pradesh. Lack of increasing age-associated seroprevalence indicates that JEV might not be immunizing in pigs which needs further investigation because models that inform public health interventions for JEV could be inaccurate if assuming long-term immunity in pigs. Although pigs are considered sentinels for human outbreaks, sufficient timeliness using sero-surveillance in pigs to inform public health interventions to prevent JEV in people will require more nuanced modelling than seroprevalence and broad climate variables alone.

The Circumstance-Driven Bivariate Integer-Valued Autoregressive Model.

The novel circumstance-driven bivariate integer-valued autoregressive (CuBINAR) model for non-stationary count time series is proposed. The non-stationarity of the bivariate count process is defined by a joint categorical sequence, which expresses the current state of the process. Additional cross-dependence can be generated via cross-dependent innovations. The model can also be equipped with a marginal bivariate Poisson distribution to make it suitable for low-count time series. Important stochastic properties of the new model are derived. The Yule-Walker and conditional maximum likelihood method are adopted to estimate the unknown parameters. The consistency of these estimators is established, and their finite-sample performance is investigated by a simulation study. The scope and application of the model are illustrated by a real-world data example on sales counts, where a soap product in different stores with a common circumstance factor is investigated.

The transmission of monetary policy shocks through the markets for reserves and money

This paper identifies supply and demand curves for bank reserves and a Divisia aggregate of monetary services within a structural vector autoregressive time-series model. Estimated over four sample periods spanning 1967 through 2020, the model illustrates how monetary policy actions can be interpreted with reference to their initial impact on bank reserves and the federal funds rate and their subsequent effects on Divisia money, nominal consumption spending, the aggregate nominal price level, and the unemployment rate. Model estimates attribute strong inflationary effects to monetary policy in the late 1960s and 1970s and also show that changes in the supply of reserves associated with the Fed's large-scale asset purchases since 2008 worked, as intended, to offset deflationary pressures and reduce unemployment. The model describes a much richer monetary policy process than one focused on interest rates alone.

Restored off‐channel pond habitats create thermal regime diversity and refuges within a Mediterranean‐climate watershed

Cool‐water habitats provide increasingly vital refuges for cold‐water fish living on the margins of their historical ranges; consequently, efforts to enhance or create cool‐water habitat are becoming a major focus of river restoration practices. However, the effectiveness of restoration projects for providing thermal refuge and creating diverse temperature regimes at the watershed scale remains unclear. In the Klamath River in northern California, the Karuk Tribe Fisheries Program, the Mid‐Klamath Watershed Council, and the U.S. Forest Service constructed a series of off‐channel ponds that recreate floodplain habitat and support juvenile coho salmon (Oncorhynchus kisutch) and steelhead (O. mykiss) along the Klamath River and its tributaries. We instrumented these ponds and applied multivariate autoregressive time series models of fine‐scale temperature data from ponds, tributaries, and the mainstem Klamath River to assess how off‐channel ponds contributed to thermal regime diversity and thermal refuge habitat in the Klamath riverscape. Our analysis demonstrated that ponds provide diverse thermal habitats that are significantly cooler than creek or mainstem river habitats, even during severe drought. Wavelet analysis of long‐term (10 years) temperature data indicated that thermal buffering (i.e. dampening of diel variation) increased over time but was disrupted by drought conditions in 2021. Our analysis demonstrates that in certain situations, human‐made off‐channel ponds can increase thermal diversity in modified riverscapes even during drought conditions, potentially benefiting floodplain‐dependent cold‐water species. Restoration actions that create and maintain thermal regime diversity and thermal refuges will become an essential tool to conserve biodiversity in climate‐sensitive watersheds.

Accurate and explainable mortality forecasting with the LocalGLMnet

Recently, accurate forecasting of mortality rates with deep learning models has been investigated in several papers in the actuarial literature. Most of the models proposed to date are not explainable, making it difficult to communicate the basis on which mortality forecasts have been made. We adapt the LocalGLMnet of Richman, R. & Wüthrich, M. V. (2023). [LocalGLMnet: Interpretable deep learning for tabular data. Scandinavian Actuarial Journal 2023(1), 71–95] to produce explainable forecasts of mortality rates using locally connected neural networks, and we show that these can be interpreted as autoregressive time-series models of mortality rates. These forecasts are shown to be highly accurate on the Human Mortality Database and the United States Mortality Database. Finally, we show how regularizing the LocalGLMnet can produce improved forecasts, and that by applying auto-encoders, observations of mortality rates can be denoised to improve forecasts even further.

Linkage vector autoregressive model

AbstractTo accommodate linkage effects of individuals, we develop a new linkage vector autoregressive (LAR) model for dynamic panel data. A main feature of the LAR model is incorporating dynamic network information in autoregressive time series modeling. The dynamic network can be given, or we can formulate the network links as a function of historical data, where unknown parameters of the function can be estimated from the data. We propose a simulation technique to check the stationarity condition of the LAR model and suggest a Bayesian Markov chain Monte Carlo method for estimation. Empirical results for the quarterly growth rates of gross domestic product (GDP) in 45 countries indicate that (i) the autoregressive (AR) coefficient for the aggregated growth rate is hard to distinguish from zero; (ii) a panel AR model with individual effects has a positive autocorrelation; and (iii) the alternative LAR models are preferred to the panel AR model. Depending on the specification of the linkage variables, the sign and size of the linkage effect can differ. The logistic linkage function has a flexible structure to accommodate the size of the linkage of individual GDP growth rates, and it strengthens the dynamics.

Research on Key Technologies for Green Transformation of Existing Residential Buildings in Dense Urban Areas

To achieve green and environmentally friendly urban construction, it is proposed to study a key technology for the green transformation of existing residential buildings in densely populated urban areas. Firstly, using a time series autoregressive model, achieve energy consumption prediction for HVAC heating. Secondly, based on multi-objective particle swarm optimization algorithm, energy-saving control of HVAC systems was achieved. Finally, the effectiveness of the proposed key technology was verified through experiments. The results of this article indicate that the green transformation of existing residential buildings in densely populated urban areas is necessary and feasible, and the application of key technologies can effectively reduce energy consumption and improve the quality of the living environment.

Latent Autoregressive Student-t Prior Process Models to Assess Impact of Interventions in Time Series

With the advent of the “Internet of Things” (IoT), insurers are increasingly leveraging remote sensor technology in the development of novel insurance products and risk management programs. For example, Hartford Steam Boiler’s (HSB) IoT freeze loss program uses IoT temperature sensors to monitor indoor temperatures in locations at high risk of water-pipe burst (freeze loss) with the goal of reducing insurances losses via real-time monitoring of the temperature data streams. In the event these monitoring systems detect a potentially risky temperature environment, an alert is sent to the end-insured (business manager, tenant, maintenance staff, etc.), prompting them to take remedial action by raising temperatures. In the event that an alert is sent and freeze loss occurs, the firm is not liable for any damages incurred by the event. For the program to be effective, there must be a reliable method of verifying if customers took appropriate corrective action after receiving an alert. Due to the program’s scale, direct follow up via text or phone calls is not possible for every alert event. In addition, direct feedback from customers is not necessarily reliable. In this paper, we propose the use of a non-linear, auto-regressive time series model, coupled with the time series intervention analysis method known as causal impact, to directly evaluate whether or not a customer took action directly from IoT temperature streams. Our method offers several distinct advantages over other methods as it is (a) readily scalable with continued program growth, (b) entirely automated, and (c) inherently less biased than human labelers or direct customer response. We demonstrate the efficacy of our method using a sample of actual freeze alert events from the freeze loss program.

Pandemic Effect on Healthcare Use and Death in Adults with Epilepsy: A Population Study.

We conducted a population-based study using Ontario health administrative data to describe trends in healthcare utilization and mortality in adults with epilepsy during the first pandemic year (March 2020-March 2021) compared to historical data (2016-2019). We also investigated if changes in outpatient visits and diagnostic testing during the first pandemic year were associated with increased risk for hospitalizations, emergency department (ED) visits, or death. Projected monthly visit rates (per 100,000 people) for outpatient visits, electroencephalography, magnetic resonance, computed tomography, all-cause ED visits, hospitalizations, and mortality were calculated based on historical data by fitting monthly time series autoregressive integrated moving-average models. Two-way interactions were calculated using Quasi-Poisson models. In adults with epilepsy during the first quarter of the pandemic, we demonstrated a reduction in all-cause outpatient visits, diagnostic testing, ED visits and hospitalizations, and a temporary increase in mortality (observed rates of 355.8 vs projected 308.8, 95% CI: 276.3-345.1). By the end of the year, outpatient visits increased (85,535.4 vs 76,620.6, 95% CI: 71,546.9-82,059.4), and most of the diagnostic test rates returned to the projected. The increase in the rate of all-cause mortality during the pandemic, compared to pre-pandemic, was greater during months with the lower frequency of diagnostic tests than months with higher frequency (interaction p-values <.0001). We described the impact of the pandemic on healthcare utilization and mortality in adults with epilepsy during the first year. We demonstrated that access to relevant diagnostic testing is likely important for this population while planning restrictions on non-urgent health services.

Trends in outpatient and inpatient visits for separate ambulatory-care-sensitive conditions during the first year of the COVID-19 pandemic: a province-based study.

The COVID-19 pandemic led to global disruptions in non-urgent health services, affecting health outcomes of individuals with ambulatory-care-sensitive conditions (ACSCs). We conducted a province-based study using Ontario health administrative data (Canada) to determine trends in outpatient visits and hospitalization rates (per 100,000 people) in the general adult population for seven ACSCs during the first pandemic year (March 2020-March 2021) compared to previous years (2016-2019), and how disruption in outpatient visits related to acute care use. ACSCs considered were chronic obstructive pulmonary disease (COPD), asthma, angina, congestive heart failure (CHF), hypertension, diabetes, and epilepsy. We used time series auto-regressive integrated moving-average models to compare observed versus projected rates. Following an initial reduction (March-May 2020) in all types of visits, primary care outpatient visits (combined in-person and virtual) returned to pre-pandemic levels for asthma, angina, hypertension, and diabetes, remained below pre-pandemic levels for COPD, and rose above pre-pandemic levels for CHF (104.8 vs. 96.4, 95% CI: 89.4-104.0) and epilepsy (29.6 vs. 24.7, 95% CI: 22.1-27.5) by the end of the first pandemic year. Specialty visits returned to pre-pandemic levels for COPD, angina, CHF, hypertension, and diabetes, but remained above pre-pandemic levels for asthma (95.4 vs. 79.5, 95% CI: 70.7-89.5) and epilepsy (53.3 vs. 45.6, 95% CI: 41.2-50.5), by the end of the year. Virtual visit rates increased for all ACSCs. Among ACSCs, reductions in hospitalizations were most pronounced for COPD and asthma. CHF-related hospitalizations also decreased, albeit to a lesser extent. For angina, hypertension, diabetes, and epilepsy, hospitalization rates reduced initially, but returned to pre-pandemic levels by the end of the year. This study demonstrated variation in outpatient visit trends for different ACSCs in the first pandemic year. No outpatient visit trends resulted in increased hospitalizations for any ACSC; however, reductions in rates of asthma, COPD, and CHF hospitalizations persisted.

Copula-based markov chain logistic regression modeling on binomial time series data

A first-order autoregressive time series model with binomial distributed random variables has been developed using the copula-based Markov chain model approach. By still utilizing conditional probability, covariate variables can also be included in the model and can be assumed as the independent variable. The time series dependent variable with a binomial distribution and continuous independent variables can be modelled using a copula-based Markov chain model with the probability of success expressed in the logit model. This study proposes a copula-based Markov chain logistic regression model with marginal binomial and joint distribution functions built through the copula function. Besides that, this study aims to estimate the parameters involved in the model. The parameters are the parameters of the logistic regression model as the relationship between the dependent and independent variables and the copula parameter as a time dependency. Using the bivariate copula functions are Clayton, Gumbel and Frank, the parameter estimation method is Maximum Likelihood Estimation (MLE). Simulations were carried out to see the efficiency of the parameter estimation and asymptotic results. Based on the simulation results, it was concluded that MLE provides an accurate estimate of the copula-based Markov chain logistic regression. In addition, the copula-based Markov chain logistic regression model can not only see the relationship between the independent and dependent variables but also provide an estimate of the time dependency of the dependent variable. The following are some of the proposed approach's highlights:•This method proposes a binomial time series data model with covariate variables by combining the logistic regression model and the first-order Markov chain model.•Parameter estimation in this model uses the Maximum Likelihood Estimation method.•The model provides the possibility to see the relationship between variables and the time dependency.

Controlling the Flexibility of Non-Gaussian Processes Through Shrinkage Priors

The normal inverse Gaussian (NIG) and generalized asymmetric Laplace (GAL) distributions can be seen as skewed and semi-heavy-tailed extensions of the Gaussian distribution. Models driven by these more flexible noise distributions are then regarded as flexible extensions of simpler Gaussian models. Inferential procedures tend to overestimate the degree of non-Gaussianity in the data and therefore we propose controlling the flexibility of these non-Gaussian models by adding sensible priors in the inferential framework that contract the model towards Gaussianity. In our venture to derive sensible priors, we also propose a new intuitive parameterization of the non-Gaussian models and discuss how to implement them efficiently in Stan. The methods are derived for a generic class of non-Gaussian models that include spatial Matérn fields, autoregressive models for time series, and simultaneous autoregressive models for aerial data. The results are illustrated with a simulation study and geostatistics application, where priors that penalize model complexity were shown to lead to more robust estimation and give preference to the Gaussian model, while at the same time allowing for non-Gaussianity if there is sufficient evidence in the data.

Feature-based and shape-match classifications of animal population time series

Estimation of long-term population trends can help population ecologists and conservation biologists assess the status and conditions of wildlife populations to inform the decision making of wildlife management and conservation. Machine learning methods such as time series clustering classify population time series into different clusters that have different trends and dynamic patterns as an alternative to statistical models. We used dynamic time warping (DTW) clustering and feature-based clustering to classify 15 rabbit population times in Mississippi, the United States from 1985 to 2005. Our feature-based method used the parameters of the order-2 Gompertz population models (or autoregressive time series models) as the features of population dynamics. We also estimated the long-term trends of the rabbit populations with the Theil-Sen analysis (TSA). The DTW clustering identified two clusters as optimal classification having the highest Silhouette score. Dynamic time warping clustering had 80% consistency in time series memberships with the TSA, whereas feature-based clustering had 87% consistency. Shape-match DTW clustering not only matches the shapes of trajectories, but also trends between time series. The features based on the Gompertz models capture trend, linear, and nonlinear dynamics. Our shape-match and feature-based time series clustering can cluster time series of different lengths and missing data. The Theil-Sen analysis generates an explicit estimate of linear trends and accounts for temporal autocorrelation. Since the true trends or patterns are often unknown, we recommend using two or all three methods of this study to assess the trends of wildlife populations.