Linear Autoregressive Model Research Articles

Assessing the Predictive Capabilities of Autoregressive Integrated Moving Average and Linear Regression Models for Acute Changes in Clinical and Selected Laboratory Parameters in Children After Cardiac Surgery in the ICU

(1) Background: The main objective of this research was to assess the clinical factors related to the condition of pediatric patients with congenital heart defects after they underwent intensive care unit surgery. The information was gathered from the Congenital Heart Disease Surgery Unit at the National Heart Foundation Hospital and Research Institute in Dhaka, Bangladesh. We gathered and examined data from 288 ICU patients. Patients under the age of twelve who required more than a 24-h ICU stay were selected. (2) Methods: The dependent and independent variables were chosen in advance based on expert opinion. The relationships between these pre-specified ICU parameters were determined using the Pearson correlation model and assessed through linear regression and ARIMA modeling to predict subsequent acute changes in the patients’ ICU statuses. (3) Results: A statistically significant relationship (p value < 0.001) was found between CVP and BP (95% CI = 0.2113; 0.353 r = 0.2841249) and between PEEP and FiO2 (95% CI = 0.6992; 0.770 r = 0.7367744). Although the relationships between pH and PO2 were minor (95% CI = 0.161; 0.308 r = 0.2362575), they were statistically significant. The parameters considered statistically significant (p < 0.001) were chosen for forecasting. In this work, the linear regression model and the ARIMA model used the parameters BP, FiO2, and PO2 for prediction. We forecasted the patients’ statuses for the next hour. It was found that the ARIMA model had a lower error rate than the linear regression model. (4) Conclusions: This study helps identify the important parameters for predicting and monitoring patients’ statuses in the ICU, with the ultimate goal of providing physicians with an early warning system to anticipate deterioration in clinical and biochemical parameters. The ability to accurately forecast future patients’ conditions can enable proactive, targeted interventions, potentially improving outcomes and reducing the risk of adverse events.

Variable selection of partially functional linear spatial autoregressive model with a diverging number of parameters

In this article, we consider variable selection of partially functional linear spatial autoregressive model with a diverging number of parameters, in which the explanatory variables include infinite dimensional predictor procedure, treated as functional data, and multiple real valued scalar variate. By combining series approximation method, two-stage least squares method and a class of non convex penalty function, we propose a variable selection method to simultaneously select significant explanatory variables in the parametric component and estimate the corresponding parameter related to spatial lag of the response variable. Under appropriate conditions, we derive the rate of convergence of the series estimator of the functional and parametric component, and show that the proposed variable selection method processes the oracle property. That is, it can estimate the zero components as exact zero with high probability, and estimate the non zero components as efficiently as if the true model was known beforehand. Simulation result show that our proposed variable selection method has better finite sample property.Notably, in the case where the correlation among the explanatory variables in the parametric component is low, the proposed variable selection method performs well. An application of the proposed variable selection method serves as a practical illustration.

Estimation in functional partially linear spatial autoregressive model

Functional regression has been a hot topic in statistical research. However, not much work has been done when response variables are cross-sectionally dependent variables and explanatory variables contain a real-valued scalar variable and a functional-valued random variable. In this paper, we consider a new functional partially linear spatial autoregressive model. Based on the functional principal components analysis and basis function approximation, we obtain the estimators of the unknown parameter and functions through the instrumental variables estimation method. The asymptotic normality and convergence rates of estimators are proved under some mild conditions. In addition, we illustrate the finite sample performance of the proposed estimation method through simulation study and a real data analysis.

A novel stochastic ProFiVaS model based on decomposition of stochastic Vasicek differential equation for modeling and simulating of financial indicators

The main purpose of this study is to develop a new discrete time stochastic ProFiVaS model based on decomposition of stochastic Vasicek differential equation which follows bouncing autoregressive AR1, with fixed variance and trend for modeling and simulating of international financial time series forecasting.This study offers the four discrete time stochastic models. The first model is determined as autoregressive integrated moving average-Arima1,1,1, and the parameter estimates of this model are found using the maximum likelihood method (MLM). Monte Carlo simulation is applied to the obtained parameters. This model is named MoCArima for short. Second, the MoCArima model whose parameters are estimated with particle swarm optimization (PSO) is determined as Proposed Monte Carlo (MC) Arima1,1,1, and is briefly named as ProMoCArima. The third model is determined as Fixed Variance Stochastic Model which has a bouncing autoregressive AR1 structure with constant variance and trend component. This model is briefly named as FiVaS. The parameter estimates are found using the MLM. The fourth model is determined as the Proposed Fixed Variance Stochastic Model. This model is briefly named as ProFiVaS. Structurally the same as the third model. The parameter estimates of both trend and stochastic parts of the FiVaS model are found by the PSO.Proposed models are applied to forecasting international different financial indicators to show its superiority and applicability. The performance and usage efficiency of the proposed four stochastic models are examined on a total of six different international financial data types, five of which are stock index data BIST100 (Türkiye), S&P500 (USA), DAX (Germany), FTSE100 (UK), NIKKEI225 (Japan), and one of which is the exchange rate EURO/USD. The ProFiVaS among all models provides the best performance on the all indices. The ProFiVaS can easily be extended to any real-world time series prediction requirements.The proposed models can be extended to all stationary and non-stationary linear or nonlinear autoregression models opening the door to modeling data types obtained from different sector fields. A part of the future plan of this work is to design a decision support system software that assigns a value of 1 when an investor needs to invest in a financial indicator, and 0 otherwise.

Assessing the Effects of Exchange Rate Volatility on Zambia’s Economic Growth: Evidence from ARDL and NARDL Models

This study investigated the interplay between exchange rate volatility, inflation rates, and real interest rates on Zambia’s economic growth from 1992 to 2022, utilizing annualized time series data. The study was necessitated by the limited published literature and relatively varying findings on the variables’ relationships in resource-dependent countries, such as Zambia. Diagnostic tests, including stationarity and co-integration analyses, were employed to determine integration orders and potential long-run relationships. The linear and nonlinear autoregressive distributed lag models were employed to assess short- and long-run dynamics of the variables on economic growth. The results established a positive short-run relationship between inflation rates and Gross Domestic Product (GDP) growth in the linear autoregressive distributive lag model, while an inverse relationship was observed in the nonlinear autoregressive distributive lag model, suggesting that negative shocks in inflation rates had a highly significant positive impact on economic growth. Furthermore, interest rates exhibited a positive relationship with economic growth, further suggesting that positive shocks had a greater significant direct effect on economic growth in comparison to negative shocks in the short and long run, respectively. Finally, exchange rates in both models exhibited an inverse relationship with economic growth irrespective of positive or negative shocks in the long run, highlighting the adverse effect of exchange rate volatility on economic growth prospects in developing countries, such as Zambia. The speed of adjustment to convergence following any disruptions was determined to be 75.18% (ARDL) and 89.19% (NARDL), highlighting relatively fast speeds of adjustments from any short-run disruptions. Notably, some of the policy recommendations included regular assessments of exchange rate volatility influences on import prices, domestic inflation, and production costs in key sectors. Additionally, the implementation of currency hedging options and forwards as well as bulking of foreign exchange reserves will ensure the stability of exchange rates against other major currencies in various economic conditions.

The Assessment of Precipitation and Droughts in the Aegean Region Using Stochastic Time Series and Standardized Precipitation Index

This study analyzes drought conditions in the Aegean region using monthly precipitation data from nine stations between 1972 and 2020. The Standardized Precipitation Index (SPI) was calculated for 1-, 3-, 6-, 9-, and 12-month periods to evaluate drought conditions at different timescales and station-specific conditions. The results indicate that short-term droughts are more frequent but shorter in duration, while longer periods exhibit fewer but more prolonged droughts. The relative frequency of drought across all periods ranges between 9% and 27%. The İzmir and Denizli stations were highlighted due to their representation of coastal and inner regions, respectively. The findings show that coastal stations, like İzmir, experience more frequent wet years compared to inner stations like Denizli, which have more dry years. Time series linear autoregressive (AR) models, using SPI-12 data, were developed to represent long-term drought trends and forecasts. The best-fitting models were determined using AIC, AICC, FPE, and Var(e) criteria, with AR(2) generally being the most suitable, except for Denizli. This integrated analysis of SPI and AR models provides a robust basis for understanding regional precipitation regimes and predicting future droughts, aiding in the development of effective drought mitigation strategies and water resource management. Future research is anticipated to extend this analysis to encompass all of Turkey and explore various time series models’ applicability.

Scalable and Interpretable Forecasting of Hydrological Time Series Based on Variational Gaussian Processes

Accurate streamflow forecasting is crucial for effectively managing water resources, particularly in countries like Colombia, where hydroelectric power generation significantly contributes to the national energy grid. Although highly interpretable, traditional deterministic, physically-driven models often suffer from complexity and require extensive parameterization. Data-driven models like Linear Autoregressive (LAR) and Long Short-Term Memory (LSTM) networks offer simplicity and performance but cannot quantify uncertainty. This work introduces Sparse Variational Gaussian Processes (SVGPs) for forecasting streamflow contributions. The proposed SVGP model reduces computational complexity compared to traditional Gaussian Processes, making it highly scalable for large datasets. The methodology employs optimal hyperparameters and shared inducing points to capture short-term and long-term relationships among reservoirs. Training, validation, and analysis of the proposed approach consider the streamflow dataset from 23 geographically dispersed reservoirs recorded during twelve years in Colombia. Performance assessment reveals that the proposal outperforms baseline Linear Autoregressive (LAR) and Long Short-Term Memory (LSTM) models in three key aspects: adaptability to changing dynamics, provision of informative confidence intervals through Bayesian inference, and enhanced forecasting accuracy. Therefore, the SVGP-based forecasting methodology offers a scalable and interpretable solution for multi-output streamflow forecasting, thereby contributing to more effective water resource management and hydroelectric planning.

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.

Dual-branch deep learning architecture for enhanced hourly global horizontal irradiance forecasting

Solar energy, a pivotal renewable resource, faces challenges posed from the inherent randomness and volatility of solar irradiance. Effective control and utilization of solar energy systems rely on the accuracy of solar irradiance prediction models. Temporal data of solar irradiance often involves a mixture of long-term patterns represented by periodicity and short-term patterns represented by nonlinearity, for which traditional approaches are difficult to balance. In this study, a novel deep learning approach employing a dual-branch architecture is proposed to forecast hourly global horizontal irradiance. The proposed model comprises two parallel branches, namely the global temporal extractor and the local temporal extractor. Two branches effectively capture complex combinations of global and local temporal patterns from multivariable input data. To enhance the effectiveness of feature extraction, the model incorporates feature-temporal attention modules and self-attention modules within the extractors, which can re-calibrate feature weights and emphasize crucial information. To strengthen the model's robustness, an autoregressive linear model is integrated in parallel, compensating for nonlinear output. The proposed model has been validated on multiple public datasets. Experimental results show the performance of the proposed model has been greatly improved, in which achieves a remarkable 41.76% improvement of forecasting accuracy over baseline models. The superiority the proposed model is also underscored through comparative analysis against state-of-the-art methods.

Estimation for partially linear single-index spatial autoregressive model with covariate measurement errors

Estimation for partially linear single-index spatial autoregressive model with covariate measurement errors

Bayesian Markov switching model for BRICS currencies' exchange rates

AbstractExchange rate modeling has always fascinated researchers because of its complex macroeconomic dynamics. This study documents the exchange rate dynamics of major emerging economies after accounting for their macroeconomic cycles and explores the Bayesian Vector Error Correction Model (VECM) Markov Regime switching model, which uses time‐varying transition probabilities. The main objective is to study the exchange rate dynamics of Brazil, Russia, India, China, and South Africa (BRICS) vis‐à‐vis the US dollar. The Bayesian setup uses two hierarchal shrinkage priors, the normal‐gamma (NG) prior and the Litterman prior, for parameters' estimation. These shrinkage priors allow for a more comprehensive assessment of the regime‐specific coefficients. The model performed well in differentiating between the two regimes for all currencies. The Russian ruble was identified to be the most depreciated currency, whereas the African Rand was the most appreciated. The evaluation of model features revealed that many regime‐specific coefficients differed significantly from their common mean. A forecasting exercise was then performed for the out‐of‐sample period to assess the model's performance. A significant improvement was observed over the basic random walk (RW) model and the linear Bayesian vector autoregression (BVAR) model.

Online feeding behavior monitoring of individual group-housed grow-finish pigs using a low-frequency RFID electronic feeding system.

Early identification of animals in need of management intervention is critical to maximize animal health and welfare and minimize issues with productivity. Feeding behavior, captured by automated feeding systems, can be used to monitor the health and welfare status of individual pigs. Here, we present a framework for monitoring feeding behavior of grow-finish pigs in real time, using a low-frequency radio frequency identification (RFID) system. Using historical data, an autoregressive linear model for predicting daily time at the feeder was developed and utilized to detect anomalous decreases in feeding behavior associated with health status of the pig. A total of 2,826 pigs were individually monitored with our warning system over the entire grow-finish period, and health warnings were compared to caretaker diagnoses. The system detected 55.7% of the caretaker diagnoses, and on average these events were detected 2.8 d earlier than diagnosis by the caretaker. High numbers of potentially spurious health warnings, generated by the system, can be partly explained by the lack of a reliable and repeatable gold standard reference data set. Results from this work provide a solid basis for monitoring individual animals, but further improvements to the system are necessary for practical implementation.

Bootstrap prediction inference of nonlinear autoregressive models

The nonlinear autoregressive (NLAR) model plays an important role in modeling and predicting time series. One‐step ahead prediction is straightforward using the NLAR model, but the multi‐step ahead prediction is cumbersome. For instance, iterating the one‐step ahead predictor is a convenient strategy for linear autoregressive (LAR) models, but it is suboptimal under NLAR. In this article, we first propose a simulation and/or bootstrap algorithm to construct optimal point predictors under an or loss criterion. In addition, we construct bootstrap prediction intervals in the multi‐step ahead prediction problem; in particular, we develop an asymptotically valid quantile prediction interval as well as a pertinent prediction interval for future values. To correct the undercoverage of prediction intervals with finite samples, we further employ predictive – as opposed to fitted – residuals in the bootstrap process. Simulation and empirical studies are also given to substantiate the finite sample performance of our methods.

The Effect of Institusional Ownership, Managerial Ownership, Profitability and Audit Quality on Tax Agressivity

The purpose of this study is to analyze the causality relationship, which explains the independent variables consisting of institutional ownership, managerial ownership, profitability and audit quality against the dependent variable of tax aggressiveness. The data analysis of this research is quantitative analysis and uses Eviews software. EViews is software used for statistical analysis and econometrics. EViews allows users to process data, test hypotheses, and create statistical models for data analysis. EViews methods include the use of time series and cross-sectional data to perform regression analysis, multivariate analysis, causality testing, and data stationary testing. EViews can also be used to design, test, and estimate econometric models such as linear regression models, autoregressive models, and mobile autoregressive models. The results of this study show that the pattern of data that has been collected and the results of testing that has been carried out using Eviews 12 with the panel data regression analysis method show that first, institutional ownership has a negative and significant effect on tax aggressiveness. Second, managerial ownership has a significant negative effect on tax aggressiveness. Third, profitability has a significantly positive effect on tax aggressiveness. Fourth, audit quality has a significant negative effect on tax aggressiveness. Keywords: institutional ownership, managerial ownership, profitability and quality checks on tax aggressiveness

Analysing the nexus between income inequality and economic growth in Ethiopia: using the non linear auto regressive distributed lag model

Analysing the nexus between income inequality and economic growth in Ethiopia: using the non linear auto regressive distributed lag model

Intraindividual time-varying dynamic network of affects: linear autoregressive mixed-effects models for ecological momentary assessment.

An interesting recent development in emotion research and clinical psychology is the discovery that affective states can be modeled as a network of temporally interacting moods or emotions. Additionally, external factors like stressors or treatments can influence the mood network by amplifying or dampening the activation of specific moods. Researchers have turned to multilevel autoregressive models to fit these affective networks using intensive longitudinal data gathered through ecological momentary assessment. Nonetheless, a more comprehensive examination of the performance of such models is warranted. In our study, we focus on simple directed intraindividual networks consisting of two interconnected mood nodes that mutually enhance or dampen each other. We also introduce a node representing external factors that affect both mood nodes unidirectionally. Importantly, we disregard the potential effects of a current mood/emotion on the perception of external factors. We then formalize the mathematical representation of such networks by exogenous linear autoregressive mixed-effects models. In this representation, the autoregressive coefficients signify the interactions between moods, while external factors are incorporated as exogenous covariates. We let the autoregressive and exogenous coefficients in the model have fixed and random components. Depending on the analysis, this leads to networks with variable structures over reasonable time units, such as days or weeks, which are captured by the variability of random effects. Furthermore, the fixed-effects parameters encapsulate a subject-specific network structure. Leveraging the well-established theoretical and computational foundation of linear mixed-effects models, we transform the autoregressive formulation to a classical one and utilize the existing methods and tools. To validate our approach, we perform simulations assuming our model as the true data-generating process. By manipulating a predefined set of parameters, we investigate the reliability and feasibility of our approach across varying numbers of observations, levels of noise intensity, compliance rates, and scalability to higher dimensions. Our findings underscore the challenges associated with estimating individualized parameters in the context of common longitudinal designs, where the required number of observations may often be unattainable. Moreover, our study highlights the sensitivity of autoregressive mixed-effect models to noise levels and the difficulty of scaling due to the substantial number of parameters.

Cramér’s moderate deviations for the LS estimator of the autoregressive processes in the neighborhood of the unit root

In this paper, we consider the linear autoregressive model with varying coefficients θn tending to the unit root. Cramér’s moderate deviations of the least-squares estimator of the parameter θn is discussed.

Model Checking in Partially Linear Spatial Autoregressive Models

This article proposes two new classes of nonparametric tests for the correct specification of linear spatial autoregressive models based on the “integrated conditional moment” approach. Our test statistics are constructed as continuous functionals of a residual marked empirical process as well as its projected version. We derive asymptotic properties of the test statistics under the null hypothesis, the alternative hypothesis, and a sequence of local alternatives. The proposed tests do not involve the selection of tuning parameters such as bandwidths and are able to detect a broad class of local alternatives converging to the null at the parametric rate n − 1 / 2 , with n being the sample size. We also propose a multiplier bootstrap procedure that is computationally simple to approximate the critical values. Monte Carlo simulations illustrate that our tests have a reasonable size and satisfactory power for different types of data-generating processes. Finally, an empirical analysis of growth convergence is carried out to demonstrate the usefulness of the tests.

Carbon volatility connectedness and the role of external uncertainties: Evidence from China

This paper investigates the volatility connectedness between China’s carbon pilot markets. Using Diebold and Yilmaz (2014)’s approach based on the time-varying parameter vector autoregression model with a variety of parameter sets, we obtain the average across 40 results to capture the volatility connectedness between the markets. We further use the linear and nonlinear autoregressive distributed lag models to assess the role of external uncertainties in shaping volatility connectedness. Several findings emerge: (1) Guangdong (Chongqing) is the largest net transmitter (receiver) in terms of volatility connectedness; (2) Volatility connectedness shows a declining trend, with its cycle fluctuations caused by compliance-driven trading; (3) Volatility connectedness correlates negatively with external uncertainties. Both economic policy and climate policy indices have impacts on volatility connectedness. We recommend introducing market makers to enhance market liquidity and reduce risk spreading. We also highlight the need for further research to pinpoint idiosyncratic factors that affect different markets.

Composite quantile regression based robust empirical likelihood for partially linear spatial autoregressive models

Composite quantile regression based robust empirical likelihood for partially linear spatial autoregressive models