First-order Autoregressive Model Research Articles

Goodness-of-fit testing in bivariate count time series based on a bivariate dispersion index

AbstractA common choice for the marginal distribution of a bivariate count time series is the bivariate Poisson distribution. In practice, however, when the count data exhibit zero inflation, overdispersion or non-stationarity features, such that a marginal bivariate Poisson distribution is not suitable. To test the discrepancy between the actual count data and the bivariate Poisson distribution, we propose a new goodness-of-fit test based on a bivariate dispersion index. The asymptotic distribution of the test statistic under the null hypothesis of a first-order bivariate integer-valued autoregressive model with marginal bivariate Poisson distribution is derived, and the finite-sample performance of the goodness-of-fit test is analyzed by simulations. A real-data example illustrate the application and usefulness of the test in practice.

Exploring the usefulness of the INLA model in predicting levels of crime in the City of Johannesburg, South Africa

Crime prediction serves as a valuable tool for deriving insightful information that can inform policy decisions at both operational and strategic tiers. This information can be used to identify high-crime areas, and optimise resource allocation and personnel management for crime prevention. Traditionally, techniques such as the Poisson model and regression analysis have been widely used for crime prediction. However, recent statistical advancements have introduced Integrated Nested Laplace Approximations (INLA) as a promising alternative for spatial and temporal data analysis. This study focuses on crime prediction using the INLA model. Specifically, the first-order autoregressive model under the INLA modelling framework is employed on longitudinal data for crime predictions in different regions of the City of Johannesburg, South Africa. The model parameters and hyperparameters considering space and time are estimated through the INLA model. In this work, the suitability and performance of the INLA model for crime prediction is assessed, which effectively captures spatial and temporal patterns. This study contributes to research by first introducing a novel approach for South African crime prediction. Secondly, it develops a model using no demographic information other than clustering attributes as an exogenous variable. Thirdly, it quantifies prediction uncertainty. Finally, it addresses data scarcity through demonstrating how INLA can provide reliable crime predictions, where conventional methods are limited. Based on our findings, the INLA model ranked areas by crime levels, obtaining a 29.3% Mean Absolute Percentage Error (MAPE) and 0.8 R2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$R^2$$\\end{document} value for crime predictions. These findings and contributions presents the potential of INLA in advancing evidence-based decision-making for crime prevention.

A novel approach for large-scale characterization of residential cooking-generated PM with computer vision and low-cost sensors

Cooking is one of the major sources of indoor particulate matter (PM), which poses significant health risks and is a severe health hazard. Current studies lack an economical and effective analytical framework for quantifying inhalable particles (PM10) and fine particulate matter (PM2.5) from residential cooking activities on a large scale under real-world scenarios. This study bridges this gap by employing computer vision (CV) technology and readily available sensors. We collected data over a month in real-world settings, including cooking videos and air quality data (indoor PM10, PM2.5, CO2, temperature, relative humidity, and outdoor PM10 and PM2.5 concentrations). To classify high-emission (pan-frying, stir-frying, deep-frying) and low-emission (stewing, steaming, boiling, non-cooking) activities, we developed and validated a robust CV model named “Cooking-I3D.” This model leverages a pre-trained Two-Stream Inflated 3D ConvNet (I3D) architecture. We then assessed the efficacy of the CV-predicted cooking method in PM characterization using a first-order multivariate autoregressive model, controlling for environmental factors. The Cooking-I3D model achieved exceptional performance, boasting an accuracy of 95 % and an Area Under the Curve (AUC) of 0.98. Our results indicate that a single 6-minute high-emission cooking event triggers a 21–25 % increase in indoor PM concentrations and a 23–24 % increase in the indoor/outdoor ratio, with relative errors in these estimates ranging from 10 to 21 %. This innovative method offers a powerful tool for long-term assessment of cooking-related indoor air pollution and facilitates precision exposure assessment in human health studies.

A Robust Approach using M-Estimation for Dynamic Panel Autoregressive Model

This paper presents a robust M-estimation approach for first-order panel autoregressive models, addressing the challenges posed by high persistence levels of the autoregressive parameter and individual heterogeneity. Generalized method of moments estimators widely used in dynamic panel models exhibit substantial finite sample biases and are sensitive to weak instruments, particularly as the autoregressive parameter gets close to unity. Our proposed weighted M-estimator, which uses a power function for the scale parameter in Huber’s loss function, offers a robust alternative. By minimizing the variance of model parameters through an optimal tuning parameter, our method enhances the efficiency and robustness of parameter estimates. We demonstrate the superiority of the proposed approach through several Monte-Carlo simulations and an application to hydro-electric power output data, providing comprehensive comparisons with existing generalized method of moments estimators.

Multiple serial correlations in global air temperature anomaly time series.

Serial correlations within temperature time series serve as indicators of the temporal consistency of climate events. This study delves into the serial correlations embedded in global surface air temperature (SAT) data. Initially, we preprocess the SAT time series to eradicate seasonal patterns and linear trends, resulting in the SAT anomaly time series, which encapsulates the inherent variability of Earth's climate system. Employing diverse statistical techniques, we identify three distinct types of serial correlations: short-term, long-term, and nonlinear. To identify short-term correlations, we utilize the first-order autoregressive model, AR(1), revealing a global pattern that can be partially attributed to atmospheric Rossby waves in extratropical regions and the Eastern Pacific warm pool. For long-term correlations, we adopt the standard detrended fluctuation analysis, finding that the global pattern aligns with long-term climate variability, such as the El Niño-Southern Oscillation (ENSO) over the Eastern Pacific. Furthermore, we apply the horizontal visibility graph (HVG) algorithm to transform the SAT anomaly time series into complex networks. The topological parameters of these networks aptly capture the long-term correlations present in the data. Additionally, we introduce a novel topological parameter, Δσ, to detect nonlinear correlations. The statistical significance of this parameter is rigorously tested using the Monte Carlo method, simulating fractional Brownian motion and fractional Gaussian noise processes with a predefined DFA exponent to estimate confidence intervals. In conclusion, serial correlations are universal in global SAT time series and the presence of these serial correlations should be considered carefully in climate sciences.

First-order multivariate integer-valued autoregressive model with multivariate mixture distributions

The univariate integer-valued time series has been extensively studied, but literature on multivariate integer-valued time series models is quite limited and the complex correlation structure among the multivariate integer-valued time series is barely discussed. In this study, we proposed a first-order multivariate integer-valued autoregressive model to characterize the correlation among multivariate integer-valued time series with higher flexibility. Under the general conditions, we established the stationarity and ergodicity of the proposed model. With the proposed method, we discussed the models with multivariate Poisson-lognormal distribution and multivariate geometric-logitnormal distribution and the corresponding properties. The estimation method based on EM algorithm was developed for the model parameters and extensive simulation studies were performed to evaluate the effectiveness of proposed estimation method. Finally, a real crime dataset was analysed to demonstrate the advantage of the proposed model with comparison to the other models.

Bivariate Random Coefficient Integer-Valued Autoregressive Model Based on a ρ-Thinning Operator

While overdispersion is a common phenomenon in univariate count time series data, its exploration within bivariate contexts remains limited. To fill this gap, we propose a bivariate integer-valued autoregressive model. The model leverages a modified binomial thinning operator with a dispersion parameter ρ and integrates random coefficients. This approach combines characteristics from both binomial and negative binomial thinning operators, thereby offering a flexible framework capable of generating counting series exhibiting equidispersion, overdispersion, or underdispersion. Notably, our model includes two distinct classes of first-order bivariate geometric integer-valued autoregressive models: one class employs binomial thinning (BVGINAR(1)), and the other adopts negative binomial thinning (BVNGINAR(1)). We establish the stationarity and ergodicity of the model and estimate its parameters using a combination of the Yule–Walker (YW) and conditional maximum likelihood (CML) methods. Furthermore, Monte Carlo simulation experiments are conducted to evaluate the finite sample performances of the proposed estimators across various parameter configurations, and the Anderson-Darling (AD) test is employed to assess the asymptotic normality of the estimators under large sample sizes. Ultimately, we highlight the practical applicability of the examined model by analyzing two real-world datasets on crime counts in New South Wales (NSW) and comparing its performance with other popular overdispersed BINAR(1) models.

Comparison of estimation and prediction methods for a zero-inflated geometric INAR(1) process with random coefficients

This study explores zero-inflated count time series models used to analyze data sets with characteristics such as overdispersion, excess zeros, and autocorrelation. Specifically, we investigate the ZIGINAR RC ( 1 ) process, a first-order stationary integer-valued autoregressive model with random coefficients and a zero-inflated geometric marginal distribution. Our focus is on examining various estimation and prediction techniques for this model. We employ estimation methods, including Whittle, Taper Spectral Whittle, Maximum Empirical Likelihood, and Sieve Bootstrap estimators for parameter estimation. Additionally, we propose forecasting approaches, such as median, Bayesian, and Sieve Bootstrap methods, to predict future values of the series. We assess the performance of these methods through simulation studies and real-world data analysis, finding that all methods perform well, providing 95% highest predicted probability intervals that encompass the observed data. While Bayesian and Bootstrap methods require more time for execution, their superior predictive accuracy justifies their use in forecasting.

Fast and asymptotically-efficient estimation in an autoregressive process with fractional type noise

This paper considers the joint estimation of the parameters of a first-order fractional autoregressive model. A one-step procedure is considered in order to obtain an asymptotically-efficient estimator with an initial guess estimator with convergence speed lower than n and singular asymptotic joint distribution. This estimator is computed faster than the maximum likelihood estimator or the Whittle estimator and therefore allows for faster inference on large samples. The paper also illustrates the performance of this method on finite-size samples via Monte Carlo simulations.

Bias correction based on AR model in spurious regression

<abstract><p>The regression of mutually independent time series, whether stationary or non-stationary, will result in autocorrelation in the random error term. This leads to the over-rejection of the null hypothesis in the conventional t-test, causing spurious regression. We propose a new method to reduce spurious regression by applying the Cochrane-Orutt feasible generalized least squares method based on a bias-corrected method for a first-order autoregressive model in finite samples. This method eliminates the requirements for a kernel function and bandwidth selection, making it simpler to implement than the traditional heteroskedasticity and autocorrelation consistent method. A series of Monte Carlo simulations indicate that our method can decrease the probability of spurious regression among stationary, non-stationary, or trend-stationary series within a sample size of 10–50. We applied this proposed method to the actual data studied by Yule in 1926, and found that it can significantly minimize spurious regression. Thus, we deduce that there is no significant regressive relationship between the proportion of marriages in the Church of England and the mortality rate in England and Wales.</p></abstract>

WHAT DRIVES MOVEMENTS IN THE INCOME VELOCITY OF MONEY? A CASE STUDY OF THE U.S.

In their efforts to stabilize the price level, central banks often rely on the growth rate in the stock of money as an intermediate target variable. Usually, the premise underlying this approach is that the income velocity of money, defined as the ratio of nominal GDP to the stock of money, either randomly fluctuates around a constant mean or can, at least, be predicted with sufficient accuracy. The purpose of this paper is to put this assumption to the test. We do so by applying a first-order autoregressive model, supplemented by a set of lagged exogenous regressors, to the quarterly changes in velocity in the U.S. Our results confirm previous findings that dynamic dependencies exist between changes in the income velocity of money over successive periods of time. They also support the assertion that rising long-term interest rates lower the demand for money. Perhaps most importantly, however, we find that all else being equal, the degree of financialization in the economy, measured by the ratio of financial assets to GDP, has a positive and statistically significant effect on velocity. A possible explanation of this finding is the increasing availability of tradable, non-monetary financial instruments that are close substitutes for bank deposits.

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.

Investor Sentiment, Financing Constraints, and Earnings Persistence

ABSTRACT Based on the background of investor sentiment volatility in the capital market, this article empirically examines the relationship between investor sentiment and corporate earnings persistence and its impact mechanism using a first-order autoregressive model with a sample of Chinese A-share non-financial listed companies from 2007 to 2019. It is found that rising investor sentiment helps improve corporate earnings persistence when investor sentiment is moderate, with financing constraints playing a part in mediating the effect. The test of heterogeneity in corporate life cycle and nature of ownership found that rising investor sentiment significantly mitigates the financing constraints in growth stage and non-state enterprises, which in turn improves their earnings persistence.

Understanding the Driving Forces of the North Pacific Victoria Mode

Abstract The Victoria Mode (VM) is defined as the second empirical orthogonal function (EOF) of sea surface temperature anomalies (SSTAs) in the North Pacific. It is independent of the Pacific decadal oscillation (PDO) and represents the second climate mode of North Pacific variability. Using a first-order autoregressive model and forcing indices that track the Aleutian low, the North Pacific Oscillation (NPO), anomalous ocean circulation in the Kuroshio–Oyashio Extension (KOE), and the cold tongue (CT) and warm pool (WP) El Niño–Southern Oscillation (ENSO), this study reconstructs the North Pacific SSTAs and examines the relative contributions of different forcing mechanisms to the VM variance. It is found that the NPO and ENSO, especially the WP ENSO, are the dominant sources of VM variability, whereas the contributions of the Aleutian low and zonal advection in the KOE region are relatively small. Further analysis shows that the forcing mechanisms acting on the VM are frequency dependent. At decadal and longer time scales, the VM variance comes mainly from the WP ENSO, whereas at interannual-time-scale contributions from the NPO and CT ENSO are important. This study suggests that the VM is an oceanic response to the NPO forcing and atmospheric teleconnections excited by ENSO events.

Research on an Underwater Target-Tracking Method Based on Zernike Moment Feature Matching

Sonar images have the characteristics of lower resolution and blurrier edges compared to optical images, which make the feature-matching method in underwater target tracking less robust. To solve this problem, we propose a particle filter (PF)-based underwater target-tracking method utilizing Zernike moment feature matching. Zernike moments are used to construct the feature-description vector for feature matching and contribute to the update of particle weights. In addition, the particle state transition method is optimized by using a first-order autoregressive model. In this paper, we compare Hu moments and Zernike moments, and we also compare whether to optimize the particle state transition on the tracking results or not based on the effects of each option. The experimental results based on the AUV (autonomous underwater vehicle) prove that the robustness and accuracy of this innovative method is better than the other combined methods mentioned in this paper.

A study on the impact of listed companies' strategies on surplus sustainability

Strategic differences have an important impact on the quality of surpluses. Based on the perspective of surplus persistence, this paper uses a total of 8917 data of A-share listed companies in Shanghai and Shenzhen in China from 2014-2019 as the research sample, and uses a first-order linear autoregressive model to explore the relationship between strategic differences and surplus persistence of listed companies, and the moderating role of property rights nature in this relationship. The study finds that the greater the strategic differences, the lower the surplus persistence; the negative relationship between strategic differences and surplus persistence is more significant in non-state-owned enterprises compared to state-owned enterprises. Further breakdown of the surplus items reveals that strategic differences affect the overall surplus persistence mainly by influencing the persistence of the accrual part of the surplus.

A sliding mode predictive anti-pitching control for a high-speed multihull

A sliding mode predictive anti-pitching control considering appendages constraints is proposed to improve the wave suppression capability of multihulls while reducing heave and pitch motions. The control method combines the advantages of model predictive control and sliding mode control to both improve the strong robustness of the system and to ensure the optimization and the ability to handle constraints explicitly. The vertical motion model is established for multihull with two types of appendages, T-foils and flaps, to achieve anti-pitching. According to the characteristics of the first-order autoregressive wave disturbance model, a low-complexity disturbance observer is devised to estimate the wave disturbance force and moment online, and combine the estimates with the prediction model to enhance the accuracy of the prediction. On this basis, a prediction model and an objective function are established with the sliding mode states as variables, and the sliding mode terminal stability constraint set is adopted to improve the stability of the closed-loop system. Last, the closed-loop system stability was analyzed based on Lyapunov stability theory. The effectiveness of the designed controller is verified by simulation and experiment, in which the multihull heave displacement is reduced by 52% and the pitch angle is reduced by 58%.

A Tweedie Markov process and its application in fisheries stock assessment

Abstract The Tweedie distribution is a useful tool to model zero-inflated non-negative continuous data. However, the Tweedie dispersion relationship (DR) is not general enough to cover some important forms such as quadratic dispersion, and an easy and fast-to-implement Tweedie AR(1) model (first-order autoregressive model) needs to be developed for spatio-temporal modelling. In this research we extend the Tweedie distribution to accommodate flexible DRs, and propose a Tweedie Markov process (TMP) with the AR(1) autocorrelation structure. This TMP is simple to implement and requires only the Tweedie probability density function. Simulation studies and real data analysis are conducted to validate our new approach.

Dynamic Modeling of Carbon Dioxide Transport through the Skin Using a Capnometry Wristband.

The development of a capnometry wristband is of great interest for monitoring patients at home. We consider a new architecture in which a non-dispersive infrared (NDIR) optical measurement is located close to the skin surface and is combined with an open chamber principle with a continuous circulation of air flow in the collection cell. We propose a model for the temporal dynamics of the carbon dioxide exchange between the blood and the gas channel inside the device. The transport of carbon dioxide is modeled by convection-diffusion equations. We consider four compartments: blood, skin, the measurement cell and the collection cell. We introduce the state-space equations and the associated transition matrix associated with a Markovian model. We define an augmented system by combining a first-order autoregressive model describing the supply of carbon dioxide concentration in the blood compartment and its inertial resistance to change. We propose to use a Kalman filter to estimate the carbon dioxide concentration in the blood vessels recursively over time and thus monitor arterial carbon dioxide blood pressure in real time. Four performance factors with respect to the dynamic quantification of the CO2 blood concentration are considered, and a simulation is carried out based on data from a previous clinical study. These demonstrate the feasibility of such a technological concept.

Maximum likelihood estimation for [formula omitted]-stable double autoregressive models

The paper investigates the maximum likelihood estimation (MLE) for a first-order double autoregressive model with standardized non-Gaussian symmetric α-stable innovation (sDAR) within a unified framework of stationary and explosive cases. It is shown that the MLE of all parameters, including the stable exponent in the innovation, are strongly consistent and asymptotically normal (with the exception of the intercept for the explosive case). Particularly, the MLE of the parameter in the conditional location is always asymptotically normal, regardless of the stationary or explosive case. This point totally differs from that for linear α-stable AR models in Andrews et al. (2009). Furthermore, it is the first time to provide exact values of the quantities related to the innovation in the asymptotic covariance matrices when the true innovation is the standard Cauchy distribution. Additionally, a modified Kolmogorov-type test statistic is proposed for model diagnostic checking in the stationary case. Monte Carlo simulation studies are conducted to confirm our theoretical findings and assess the finite-sample performance of the MLE and the modified Kolmogorov-type test. An empirical example is analyzed to illustrate the usefulness of sDAR models.