Autoregressive Time Series Models Research Articles

Vector time series analysis on economic growth and financial growth based on the oil price

In this paper, we consider the Europe oil prices, Brent, West Texas Intermediate, WTI, American stock market index based on the market capitalizations of 500 large companies having common stock listed on the NYSE or NASDAQ, S & P 500 , and the real gross domestic product, GDP. Based on the rolling test of Granger causality, the Europe oil prices data does Granger-cause the real gross domestic product data and S & P 500 data. So, the vector autoregressive model can be suggested. The one-step prediction method selects the vector autoregressive model as the optimal model for GDP data and S & P 500 data. The main purpose of this paper is to select the optimal model (and variable) based on Vuong’s model selection test. So, we consider the estimation and model selection of the vector autoregressive time series model with Normal innovation. The maximum likelihood method is proposed for the estimation of unknown parameters. We provide Vuong’s test for order and model selection, i.e. for selecting the order and a suitable subset of regressors, in a vector autoregressive model. Our results show that Vuong’s test confirms the causality test for GDP and S & P 500 data. Also, the results of Vuong’s test confirms the results of the predictive method.

Model predictive control of a single-buoy wave energy converter with coupled constraints and model adaptation

A novel optimization framework is introduced for a single-buoy wave energy converter (WEC), which integrates model predictive control (MPC) with the boundary element method (BEM). A time-series auto-regressive (AR) model is employed to predict the wave excitation force in the near future for the MPC algorithm, and its accuracy is evaluated. Incorporation of an AR wave prediction model within the MPC framework significantly enhances operational efficiency and reduces computational costs. Application of a quadratic viscous damping correction and quantification of the prediction horizon effectively mitigated model mismatch between the linearized state-space idealization utilized within the optimizer and the actual controlled WEC. Mitigation of model mismatch significantly enhances prediction accuracy and broadens the applicability of the MPC. A sensitivity analysis is performed, and the coupled effects between constraints are examined to determine an optimal performance benchmark. The imposition of constraints on power take-off (PTO) force variation within the MPC framework ensures system resilience, indicating the practical feasibility of the approach. Simulations based on conditions typical of Zhaitang Island, China, suggest that employing an MPC algorithm for the WEC can increase maximum energy capture efficiency by 20% compared to optimal passive control. The MPC is shown to adjust the device behavior in response to varying sea conditions and to optimize performance for each sea state.

Abstract 4136911: Daily Dyadic Symptom Appraisal Dynamics During Care Transitions in Persons with Heart Failure and Their Care Partners

Background: Symptom monitoring after heart failure (HF) hospitalization is a central aspect of patient education. However, appraising symptoms can be difficult for persons with HF (PWHFs), and studies suggest family care partners (CPs) play a key supportive role. The purpose of this study is to examine dyadic HF symptom appraisal dynamics in PWHF-CP dyads during hospital-to-home transitions. Methods: We conducted a daily diary study of dyadic symptom appraisal in which PWHFs and CPs were enrolled during a HF hospitalization. Over 5 weeks, both completed daily assessments of the PWHF’s symptoms (HF Somatic Perception Scale, PROMIS Fatigue 4a). Each dyad’s appraisal dynamics were quantified using a set of N of 1 dyadic autoregressive time series models examining total symptoms, hallmark symptoms (dyspnea, edema) and nonspecific symptoms (early/subtle cluster, fatigue). Models were examined for within-dyad dynamics (within-dyad associations on the same day or on a 1-day lag). Patterns in significant dynamics across dyads were narratively described. Results: This analysis includes n=14 cohabitating dyads, all partnered. On average, PWHFs and CPs were 69.6±5.4 and 67.4±8.0 years of age. The sample was relatively gender balanced (43% of PWHFs and 64% of CPs identified as female), and primarily identified as non-Hispanic (86% of PWHFs, 93% of CPs) and White (93% of PWHFs, 86% of CPs). Most PWHFs had non-ischemic cardiomyopathy (64%) and were NYHA Class III/IV (86%), with 57% HFrEF (mean EF 37%±17%). Symptom appraisals were highly variable within and across dyads (Fig 1). Most (n=11, 79%) had significant dyadic dynamics, but dynamics across dyads varied by symptom type and time structure (Fig 2). Conclusions: The types of symptoms that HF care dyads are able to appraise together and the time structure of appraisals are variable during care transitions. Precision approaches tailored to individual dyads are needed to optimize inclusion of CPs in symptom monitoring interventions.

Maximum-likelihood estimation of the Po-MDDRCINAR(p) model with analysis of a COVID-19 data

Integer-valued data are frequently encountered in time series studies. A pth-order mixed dependence-driven random coefficient integer-valued autoregressive time series model (Po-MDDRCINAR(p)) in view of binomial and negative binomial operators, where the innovation sequence follows a Poisson distribution, is investigated to provide meaningful theoretical explanations. Strict stationary and ergodicity of the model are demonstrated. Furthermore, the conditional least-squares and conditional maximum-likelihood methods are adopted to estimate the parameters, where the asymptotic characterization of the estimators is derived. Finite-sample properties of the conditional maximum-likelihood estimator are examined in relation to the widely used conditional least-squares estimator. The conclusion is that, if the Poisson assumption of the innovation sequence can be justified, conditional maximum-likelihood method performs better in terms of MADE and MSE. Finally, the practical performance of the model is illustrated by a set of COVID-19 data of suspected cases in China with a comparison with relevant models that exist so far in the literature.

The Vasicek distribution autoregressive time-series model for aggregated data of default and delinquency rates

Abstract Is it possible to analyse time series of aggregated data of default and delinquency rates with a simple model that includes both cross-sectional and serial dependence? To address this question, this paper proposes an autoregressive time-series model for Vasicek-distributed random variables. A direct result from the proposed model is that it leads to a novel out-of-time validation test for aggregated default and delinquency rates. The motivation for the model comes from an analysis of a time series of aggregated US credit card delinquencies, for which the Poisson or binomial distribution cannot be used. The proposed model can also be employed to analyse a time series of the average default probability of a portfolio.

Correction to: A Smooth Transition Autoregressive Model for Matrix-Variate Time Series

Correction to: A Smooth Transition Autoregressive Model for Matrix-Variate Time Series

Diagnostic checking of periodic vector autoregressive time series models with dependent errors

In this article, we study the asymptotic behaviour of the residual autocorrelations for periodic vector autoregressive time series models (PVAR henceforth) with uncorrelated but dependent innovations (i.e., weak PVAR). We then deduce the asymptotic distribution of the Ljung–Box-McLeod modified Portmanteau statistics for weak PVAR models. In Monte Carlo experiments, we illustrate that the proposed test statistics have reasonable finite sample performance. When the innovations exhibit conditional heteroscedasticity or other forms of dependence, it appears that the standard test statistics (under independent and identically distributed innovations) are generally unreliable, overrejecting, or underrejecting severely, while the proposed test statistics offer satisfactory levels. The proposed methodology is employed in the analysis of two river flows.

Refining Estimation of the Instantaneous Reproduction Number During Early Pandemic Stages: Addressing Case-Reporting Variability and Serial Interval Uncertainty.

During infectious disease outbreaks, estimates for the instantaneous reproduction number, R(t), are essential for understanding transmission dynamics. This study develops and analyzes new methodology to improve estimation of R(t) when observed case counts are subject to reporting patterns and available serial interval estimates are subject to uncertainty and non-representativeness. Specifically, we developed a Bayesian time-since-infection model with layers to adjust for reporting measurement error, integrate multiple candidate serial interval estimates, and estimate transmission with an autoregressive time-series model incorporating factors relevant to transmission. Additionally, we provide practical tools to identify reporting patterns and determine when to smooth case counts for more usable R(t) estimates. We evaluated model performance relative to widely adopted methodology by simulating outbreak data, finding improved R(t) estimation with the proposed methodology. We also used 2020 COVID-19 data to analyze transmission trends and predictors, identifying strong day-of-week and social distancing effects that subsequently reduced estimate volatility. In addition to new approaches for addressing serial interval uncertainty and incorporating transmission predictor information, this study provides an alternative approach for addressing case-reporting patterns without delaying detection or smoothing over relevant transmission signals. These tools and findings may be used or built upon for current and future outbreaks.

Addressing multidimensional highly correlated data for forecasting in precision beekeeping

In recent years, there have been relevant advances in precision beekeeping. These advances are mainly focused on proposing sensor systems that collect crucial information for bee welfare, creating integrated architectures that allow beekeepers to monitor the current state of their hive through real-time data. However, there is a lack of predictive models that would allow beekeepers to anticipate specific events that endanger bee welfare and lead to a decline in productivity. Specifically, predictive approaches accounting for the high correlation among internal variables of beehives have not been developed to date. To address this research gap, multivariate predictive models, including auto-regressive state-space and time series models, have been implemented and applied to four different hives from the we4bee project. These models aim to predict the internal variables of beehives (four different temperatures, humidity, and weight) by utilizing the meteorological conditions to which the hives are exposed. A cross-validation adapted to time series data was employed for model generalization assessment. Prediction models based on vector time series exhibited superior performance in forecasting internal hive variables compared to multivariate auto-regressive state-space models. Overall, the approach based on the vector error correction model yielded the best balance between fit, prediction, and computational cost. The VEC-based approach produces predictions with maximum mean absolute errors of 177 (312)g in weight, 3.366 (3.802)% in humidity, and 1.122 (1.685)°C in temperature at 1 (3)-days ahead when dealing with beehives exhibiting a high degree of correlation in their internal variables. Moreover, the VEC-based approach requires less than a second to perform the time series fitting process, which makes it particularly interesting for application in big data environments. The integration of such models into a decision support system would meet the need of beekeepers to anticipate potential threats to the welfare of their bee colonies, streamlining their monitoring processes while eliminating the need for continuous inspections.

Longer-term impacts of the COVID-19 pandemic on obstructive sleep apnoea (OSA)-related healthcare: a province-based study

RationaleFollowing marked reductions in sleep medicine care early in the COVID-19 pandemic, there is limited information about the recovery of these services. We explored long-term trends in obstructive sleep apnoea...

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.

Exponential stochastic volatility model with Laplace returns and its variants

This paper explores the exponential stochastic volatility model generated by first-order exponential Markov sequences to model financial time series. The stationary exponential Markov sequences used to generate the volatility model are the linear exponential autoregressive model, minification model, new exponential autoregressive time series model, and an exponential mixture of autoregressive and minification processes. The statistical properties of the models are studied and the estimation of model parameters is carried out using the generalized method of moments. An approximate Kalman filtering method and a non-linear filtering approach are employed to diagnose the models. To verify the correctness of the estimations, simulation studies are conducted, and two real datasets are used to demonstrate how the models are applied. Furthermore, a comparison of the suggested models is performed using the measures root mean square error, mean absolute error, and Value at Risk via a backtesting procedure.

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

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.

Leveraging VQ-VAE tokenization for autoregressive modeling of medical time series

In this work, we present CodeAR, a medical time series generative model for electronic health record (EHR) synthesis. CodeAR employs autoregressive modeling on discrete tokens obtained using a vector quantized-variational autoencoder (VQ-VAE), which addresses key challenges of accurate distribution modeling and patient privacy preservation in the medical domain. The proposed model is trained with next-token prediction instead of a regression problem for more accurate distribution modeling, where the autoregressive property of CodeAR is useful to capture the inherent causality in time series data. In addition, the compressive property of the VQ-VAE prevents CodeAR from memorizing the original training data, which ensures patient privacy. Experimental results demonstrate that CodeAR outperforms the baseline autoregressive-based and GAN-based models in terms of maximum mean discrepancy (MMD) and Train on Synthetic, Test on Real tests. Our results highlight the effectiveness of autoregressive modeling on discrete tokens, the utility of CodeAR in causal modeling, and its robustness against data memorization.

Negative binomial community network vector autoregression for multivariate integer-valued time series

Modeling multivariate integer-valued time series with appropriate methods is currently a popular research topic. In this paper, we propose a multivariate integer-valued autoregressive time series model based on a fixed network community structure. We use the negative binomial distribution as the conditional marginal distribution and a copula to construct the conditional joint distribution. The newly proposed model introduces the heterogeneity of nodes. Stability conditions are provided for both fixed and increasing dimensions. We estimate the parameters of the proposed model by maximizing the quasi-likelihood function with known and unknown community membership matrices, respectively. Corresponding asymptotic properties of parameter estimates are also provided. A simulation study is conducted to demonstrate the asymptotic behavior of the proposed model, and two real datasets are employed to compare the proposed model with other competitive models.

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.