Autoregressive Time Series Models Research Articles

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.

Active sensing ultrasonic guided wave-based damage diagnosis via stochastic stationary time-series models

In the context of acousto-ultrasonic guided wave-based structural health monitoring, a statistical damage detection and identification (collectively referred to as damage diagnosis) framework for metallic and composite materials is proposed. Stochastic stationary time-series autoregressive (AR) models are used to model the ultrasonic wave propagation between piezoelectric actuator-sensor pairs on structural components and enable the damage diagnosis process via the use of the AR estimated parameters and corresponding covariance matrices. The proposed method exploits guided wave signals including the reflection parts, and thus the extraction of the S0 and/or A0 modes is not necessary, while the statistical properties and variation of estimated model parameters with respect to damage intersecting and non-intersecting wave propagation paths are presented and assessed. To investigate the method’s performance and robustness, two variations are proposed based on the singular value decomposition and principal component analysis. The obtained modified AR parameter vectors are then used to estimate appropriate statistical characteristic quantities used to enable the damage detection and identification tasks. The diagnosis is based on properly defined statistical hypotheses decision-making schemes and predetermined type I error probabilities. The performance and applicability of the method are explored experimentally via a series of tests on aluminum and composite coupons under various damage scenarios for damage intersecting and non-intersecting paths. The results of the present study demonstrated the effectiveness and robustness of the proposed modeling and diagnostic framework for guided wave-based damage diagnosis that can be implemented in a potentially automated way.

Prediction of comprehensive dynamic performance for probability screen based on AR model-box dimension

In order to evaluate the comprehensive dynamic performance of probability screen and select the appropriate working conditions, a dynamic model of probability screen vibration system is established. Then, the calculation method of the dynamic characteristic parameters, based on the time series Auto Regression (AR) model of vibration test, is used. The relationship among the comprehensive dynamic characteristics, the screening efficiency and the box dimension of probability screen vibration system is analyzed, and Least Square Support Vector Machine (LSSVM), Generalized Regression Neural Network (GRNN) and Back Propagation Neural Network (BPNN) are used to predict the screening efficiency with box dimension. The analysis result shows that the screening efficiency, the stability, the response rapidity and the comprehensive dynamic characteristic of the system are all related to the box dimension of time series. As for the complexity of probability screen vibration system, it affects the comprehensive dynamic performance, and ultimately touches the screening efficiency of the probability screen; The best working conditions for the system are selected by the curve between box dimension and the working condition parameter; Taking box dimension as the only input variable, the prediction accuracy of the screening efficiency is high by using LSSVM,GRNN and BPNN methods, the prediction results are stable and reliable, and the box dimension can be used as a single input variable to predict the screening efficiency, it has the advantages of fewer input parameters, high prediction efficiency, and high prediction accuracy, which has great potential for expanding application space and further research value.

Comparative evaluation of daily streamflow prediction by ANN and SWAT models in two karst watersheds in central south Texas

Abstract This work compares the accuracy of streamflow estimated by a data-driven artificial neural network (ANN) and the physically based soil and water assessment tool (SWAT). The models were applied in two small watersheds, one highly urbanized and the other primarily covered with evergreen forest and shrubs, in the San Antonio region of central south Texas, where karst geologic features are prevalent. Both models predicted daily streamflow in the urbanized watershed very well, with the ANN and SWAT having the Nash–Sutcliffe coefficient of efficiency (NSE) values of 0.76 and 0.72 in the validation period, respectively. However, both models predicted streamflow poorly in the nonurban watershed. The NSE values of the ANNs significantly improved when a time series autoregressive model structure using historical streamflow data was implemented in the nonurban watershed. The SWAT model only achieved trivial performance improvement after using the SWAT-CUP SUFI-2 calibration procedure. This result suggests that an ANN model may be more suitable for short-term streamflow forecasting in watersheds heavily affected by karst features where the complex processes of rapid groundwater recharge and discharge strongly influence surface water flow.

High-dimensional low-rank tensor autoregressive time series modeling

Modern technological advances have enabled an unprecedented amount of structured data with complex temporal dependence, urging the need for new methods to efficiently model and forecast high-dimensional tensor-valued time series. This paper provides a new modeling framework to accomplish this task via autoregression (AR). By considering a low-rank Tucker decomposition for the transition tensor, the proposed tensor AR can flexibly capture the underlying low-dimensional tensor dynamics, providing both substantial dimension reduction and meaningful multi-dimensional dynamic factor interpretations. For this model, we first study several nuclear-norm-regularized estimation methods and derive their non-asymptotic properties under the approximate low-rank setting. In particular, by leveraging the special balanced structure of the transition tensor, a novel convex regularization approach based on the sum of nuclear norms of square matricizations is proposed to efficiently encourage low-rankness of the coefficient tensor. To further improve the estimation efficiency under exact low-rankness, a non-convex estimator is proposed with a gradient descent algorithm, and its computational and statistical convergence guarantees are established. Simulation studies and an empirical analysis of tensor-valued time series data from multi-category import-export networks demonstrate the advantages of the proposed approach.

Probabilistic Intraday Wastewater Treatment Plant Inflow Forecast Utilizing Rain Forecast Data and Sewer Network Sensor Data

AbstractForecasting of wastewater treatment plant inflow dynamics constitutes an enabler technology for wastewater treatment process optimization using model predictive control. However, accurate inflow prediction is still challenging, especially for strong rainfall events, where complex system dynamics and missing information on future rainfall represent limiting factors. We propose a seasonal probabilistic time series model for modeling the short‐term wastewater inflow accurately while providing quantification of forecast uncertainty. To ensure suitability for practical implementation, the unconstrained parameters of the predictive distribution are modeled as linear functions of the input variables in the framework of Generalized Additive Models for Location Scale and Shape. Non‐linear effects are approximated by Rectified Linear Units, accounting for buffering within the sewer network and flow‐dependent catchment response time. In addition to water level measurements from within the sewer network and rain rate measurements, rain forecasts are incorporated as exogenous regressors, where historical rain forecasts are used for model calibration. The model performance is evaluated on historical data from a German wastewater treatment plant using deterministic and probabilistic scoring rules. We benchmark against an autoregressive time series model and a long short‐term memory artificial neural network. Our results show that the proposed model unites the benefits of high prediction accuracy of the neural network and enhanced intelligibility of the autoregressive model, but accurate real‐time rain forecasts are mandatory for successful real‐world implementation.

Computationally Efficient Poisson Time-Varying Autoregressive Models through Bayesian Lattice Filters

Estimation of time-varying autoregressive models for count-valued time series can be computationally challenging. In this direction, we propose a time-varying Poisson autoregressive (TV-Pois-AR) model that accounts for the changing intensity of the Poisson process. Our approach can capture the latent dynamics of the time series and therefore make superior forecasts. To speed up the estimation of the TV-AR process, our approach uses the Bayesian Lattice Filter. In addition, the No-U-Turn Sampler (NUTS) is used, instead of a random walk Metropolis–Hastings algorithm, to sample intensity-related parameters without a closed-form full conditional distribution. The effectiveness of our approach is evaluated through model-based and empirical simulation studies. Finally, we demonstrate the utility of the proposed model through an example of COVID-19 spread in New York State and an example of US COVID-19 hospitalization data.

Heliostat-field soiling predictions and cleaning resource optimization for solar tower plants

One of the primary cost drivers for concentrated solar power operations and maintenance is the soiling of heliostats in the solar field. Although this loss can be largely recovered through cleaning operations, the associated costs are substantial and require careful consideration in relation to productivity gains.This paper presents a novel methodology for characterizing soiling losses through experimental measurements. Soiling predictions were obtained by calibrating a soiling model based on field measurements from a 50 MW modular solar tower project in Mount Isa, Australia. The study found that the mean predicted soiling rate for horizontally fixed mirrors was 0.12pp/d during low dust seasons and 0.22pp/d during high seasons. Autoregressive time series models were employed to extend two years of onsite meteorological measurements to a 10-year period, enabling the prediction of heliostat-field soiling rates. A fixed-frequency cleaning heuristic was applied to optimize the cleaning resources for various operational policies by balancing direct cleaning resource costs against the expected lost production, which was computed by averaging multiple simulated soiling loss trajectories. Analysis of resource usage showed that the cost of fuel and operator salaries contributed 42% and 35% respectively towards the cleaning cost. In addition, stowing heliostats in the horizontal position at night increased daily soiling rates by 114% and the total cleaning costs by 51% relative to vertically stowed heliostat-field. Under a simplified night-time-only power production configuration, the oversized solar field effectively charged the thermal storage during the day, despite reduced mirror reflectance due to soiling. These findings suggest that the plant can maintain efficient operation even with a reduced cleaning rate. Finally, it was observed that performing cleaning operations during the day led to a 7% increase in the total cleaning cost compared to a night-time cleaning policy. This was primarily attributed to the need to park operational heliostats for cleaning.

Estimation of Runoff Using USDA SCS-Curve Number and Autoregressive Time Series Model Parameters for Kachhinda Watershed, Morena District, Madhya Pradesh, India

Hydrological modeling is an influential method for examining hydrologic systems, serving as a valuable tool in investigating these systems for both present studies involving two hydrologic runoff models viz. Soil Conservation Service Two methods, namely the Soil Conservation Service-Curve Number (SCS-CN) method and the Autoregressive Time Series model, were utilized in the Kachhinda watershed to estimate surface runoff, CN, and AMC conditions. The study area covers 600 hectares and is sited in Morena district of M.P. in Chambal division. The SCS-CN technique was employed to determine the curve number and estimate surface runoff by using the potential maximum retention. The CN of the watershed was calculated and compared to observed and estimated surface runoff, which were found to be in close agreement with each other. Additionally, an Autoregressive Time Series model was developed to establish the correlation between observed and estimated runoff, resulting in a correlation coefficient of 0.974. Different orders of AR time series models (0, 1, and 2) were tested to predict annual stream flow, and the model goodness of fit was evaluated using the Box-Pierce Portmanteau test and the Akaike Informations Principle. The Akaike Information Criterions value for the Autoregressive (1) model for runoff was found to be 0.919158, which is within the range of the values obtained for Autoregressive (0) (0.207433) and Autoregressive (2) (5.9767) models.

A Test of the Behavioral Model of Tic Disorders Using a Dynamical Systems Framework

Tic disorders are a class of neurodevelopmental disorders characterized by involuntary motor and/or vocal tics. It has been hypothesized that tics function to reduce aversive premonitory urges (i.e., negative reinforcement) and that suppression-based behavioral interventions such as habit reversal training (HRT) and exposure and response prevention (ERP) disrupt this process and facilitate urge reduction through habituation. However, previous findings regarding the negative reinforcement hypothesis and the effect of suppression on the urge-tic relationship have been inconsistent. The present study applied a dynamical systems framework and within-subject time-series autoregressive models to examine the temporal dynamics of urges and tics and assess whether their relationship changes over time. Eleven adults with tic disorders provided continuous urge ratings during separate conditions in which they were instructed to tic freely or to suppress tics. During the free-to-tic conditions, there was considerable heterogeneity across participants in whether and how the urge-tic relationship followed a pattern consistent with the automatic negative reinforcement hypothesis. Further, little evidence for within-session habituation was seen; tic suppression did not result in a reduction in premonitory urges for most participants. Analysis of broader urge change metrics did show significant disruption to the urge pattern during suppression, which has implications for the current biobehavioral model of tics.

Modeling the Asymmetric Reinsurance Revenues Data using the Partially Autoregressive Time Series Model: Statistical Forecasting and Residuals Analysis

The autoregressive model is a representation of a certain kind of random process in statistics, insurance, signal processing, and econometrics; as such, it is used to describe some time-varying processes in nature, economics and insurance, etc. In this article, a novel version of the autoregressive model is proposed, in the so-called the partially autoregressive (PAR(1)) model. The results of the new approach depended on a new algorithm that we formulated to facilitate the process of statistical prediction in light of the rapid developments in time series models. The new algorithm is based on the values of the autocorrelation and partial autocorrelation functions. The new technique is assessed via re-estimating the actual time series values. Finally, the results of the PAR(1) model is compared with the Holt-Winters model under the Ljung-Box test and its corresponding p-value. A comprehensive analysis for the model residuals is presented. The matrix of the autocorrelation analysis for both points forecasting and interval forecasting are given with its relevant plots.

Margin‐closed vector autoregressive time series models

Conditions are obtained for a Gaussian vector autoregressive time series of order , VAR(), to have univariate margins that are autoregressive of order or lower‐dimensional margins that are also VAR(). This can lead to ‐dimensional VAR() models that are closed with respect to a given partition of by specifying marginal serial dependence and some cross‐sectional dependence parameters. The special closure property allows one to fit the subprocesses of multi‐variate time series before assembling them by fitting the dependence structure between the subprocesses. We revisit the use of the Gaussian copula of the stationary joint distribution of observations in the VAR() process with non‐Gaussian univariate margins but under the constraint of closure under margins. This construction allows more flexibility in handling higher‐dimensional time series and a multi‐stage estimation procedure can be used. The proposed class of models is applied to a macro‐economic data set and compared with the relevant benchmark models.

Nonlinear semiparametric autoregressive models based on a class of two-piece distributions

In this study, we examined the well-known nonlinear autoregressive time series model in which innovations follow the flexible class of two-piece distributions based on the scale mixtures of normal (TP-SMN) family. The mentioned class of distributions is a rich class of distributions family that covers the robust symmetric/asymmetric light/heavy-tailed distributions. The nonlinear part of the autoregressive time series model is estimated via the semiparametric and nonparametric curve estimation based on the conditional least square method and nonparametric kernel approach. The maximum likelihood (ML) estimates of the model parameters, using a suitable hierarchical representation of the TP-SMN family on the model are obtained via an expectation-maximization type algorithm. Performances and usability of the proposed model and estimates are shown through simulation studies and a real dataset.