Jumps in binomial AR(1) processes

We consider the binomial AR(1) model for serially dependent processes of binomial counts. After a review of its definition and known properties, we investigate marginal and serial properties of jumps in such processes. Based on these results, we propose the jumps control chart for monitoring a binomial AR(1) process. We show how to evaluate the performance of this control chart and give design recommendations.     

Statistical Inference for the Covariates-driven Binomial AR(1) Process

Acta Mathematicae Applicatae Sinica, English Series - The binomial autoregressive (BAR(1)) process is very useful to model the integer-valued time series data defined on a finite range. It is...     

Empirical Likelihood Inference for AR（p） Model

In this article we study the empirical likelihood inference for AR（p） model. We propose the moment restrictions, by which we get the empirical likelihood estimator of the model parametric, and we also propose an empirical log-likelihood ratio base on this estimator. Our result shows that the EL estimator is asymptotically normal, and the empirical log-likelihood ratio is proved to be asymptotically standard chi-squared.     

On AR(1) models with periodic and almost periodic coefficients

This paper is concerned with the existence of bounded solutions to the system of equations X_n=a_nX_n−1+ξ_n, nZ, where ξ_n are uncorrelated constant variance zero mean random variables. We give necessary and sufficient conditions for boundedness in the general case and then specifically for periodic and almost periodic (a_n). This provides the first step in extending the periodic autoregressive models, for which boundedness is equivalent to the stationarity of the blocked vector sequence

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to the almost periodic case.     

Inference for the Lee-Carter Model With An AR(2) Process

Methodology and Computing in Applied Probability - Researchers in studying longevity risk often employ the Lee-Carter model with a unit root AR(1) process for unobserved mortality indexes. When one...     

Robust goodness-of-fit tests for AR(p) models based onL 1-norm fitting

A robustified residual autocorrelation is defined based onL ₁-regression. Under very general conditions, the asymptotic distribution of the robust residual autocorrelation is obtained. A robustified portmanteau statistic is then constructed which can be used in checking the goodness-of-fit of AR(p) models when usingL ₁-norm fitting. Empirical results show thatL ₁-norm estimators and the proposed portmanteau statistic are robust against outliers, error distributions, and accuracy for a given finite sample. Project supported by the Foundation of State Educational Commission and a research grant from the Doctoral Program Foundation of China (#97000139).     

Monitoring parameter change in AR(p) time series models

Sequential tests that are generalizations of Page’s CUSUM tests are proposed for detecting an abrupt change in any parameter, or in any collection of parameters of an autoregressive time series model. These tests accommodate nuisance parameters. They are based on large sample approximations to the efficient score vector under the null hypothesis of no change and under the alternative. The empirical power of the tests is evaluated in a simulation study. The new method performs better than the existing ones found in the literature if the criterion is the type I error probability, which can be unacceptably high for methods that minimize the expected value of the reaction time.     

Trimmed stable AR(1) processes

In this paper we investigate the distribution of trimmed sums of dependent observations with heavy tails. We consider the case of autoregressive processes of order one with independent innovations in the domain of attraction of a stable law. We show if the $d$ largest (in magnitude) terms are removed from the sample, then the sum of the remaining elements satisfies a functional central limit theorem with random centering provided $d=d\left(n\right)\ge n^{\gamma }$ (for some $\gamma >0$) and $d\left(n\right)/n\to 0$. This result is used to get asymptotics for the widely used CUSUM process in case of dependent heavy tailed observations.     

Minimum Distance Estimation in AR(1)-processes

In this paper a new minimum distance estimator is defined in case that the residuals of an AR(1)-process are contaminated normally distributed. This estimator is asymtotically normally distributed and in most cases less biased than the least square estimator. Furthermore, a method is presented to numerically calculate the minimum distance estimator as a root of an implicit function.     

m维AR(p)模型的统计诊断

统计诊断就是探查对统计推断（如估计或预测等）有较大影响的数据从而对全过程数据进行诊断．本文应用基于数据删除模型得到二维AR（1）模型的参数估计诊断公式,给出了Cook统计量的计算公式,进而推广到m维AR（p）模型的情形．     

Asymptotic behaviour of the least squares estimator of the mean of AR(1) models

The aim of the paper is to investigate the limit behaviour of the least squares estimator of the shift parameter of nearly unstable, nearly stable, and nearly explosive AR(1) models. Both zero start and stationary cases are treated. Connection with the maximum likelihood estimator of the shift parameter of continuous time AR(1) processes is also discussed.     

Heteroscedasticity and/or Autocorrelation Checks in Longitudinal Nonlinear Models with Elliptical and AR（1） Errors

The aim of this paper is to study the tests for variance heterogeneity and/or autocorrelation in nonlinear regression models with elliptical and AR(1) errors. The elliptical class includes several symmetric multivariate distributions such as normal, Student-t, power exponential, among others. Several diagnostic tests using score statistics and their adjustment are constructed. The asymptotic properties, including asymptotic chi-square and approximate powers under local alternatives of the score statistics, are studied. The properties of test statistics are investigated through Monte Carlo simulations. A data set previously analyzed under normal errors is reanalyzed under elliptical models to illustrate our test methods.     

Asymptotic inference for AR(1) panel data

A general asymptotic theory is given for the panel data AR(1) model with time series independent in different cross sections. The theory covers the cases of stationary process, local to unity process, unit root process, mildly integrated, mildly explosive and explosive processes. It is assumed that the cross-sectional dimension and time-series dimension are respectively N and T. The results in this paper illustrate that whichever the process is, with an appropriate regularization, the least squares estimator of the autoregressive coefficient converges in distribution to a normal distribution with rate at least O(N-1/3). Since the variance is the key to characterize the normal distribution, it is important to discuss the variance of the least squares estimator. We will show that when the autoregressive coefficient ρ satisfies |ρ| 1, the variance declines at the rate O((NT)-1), while the rate changes to O(N~(-1) T~(-2)) when ρ = 1 and O(N~(-1)ρ~(-2 T+4)) when |ρ| 1. ρ = 1 is the critical point where the convergence rate changes radically. The transition process is studied by assuming ρ depending on T and going to 1. An interesting phenomenon discovered in this paper is that, in the explosive case, the least squares estimator of the autoregressive coefficient has a standard normal limiting distribution in the panel data case while it may not has a limiting distribution in the univariate time series case.     

Arbitrary elementary landscapes & AR(1) processes

Neighborhood specification is a dominant consideration in assuring the success of a direct search approach to a difficult combinatorial optimization problem. Previous research has shown the efficacy of imposing an elementary landscape upon the search topology. Barnes et al. [J.W. Barnes, S. Dokov, B. Dimova, A. Solomon, A theory of elementary landscapes, Applied Mathematics Letters 16 (2003)] generalize the notion of elementary landscapes to embrace arbitrary neighborhood digraphs. Stadler [P.F. Stadler, Landscapes and their correlation functions, Journal of Mathematical Chemistry 20 (1996)] shows, for the special case of symmetric-regular neighborhood digraphs, that the autocorrelation function associated with a smooth elementary landscape is consistent with an AR(1) time series. In this paper, we extend this idea to arbitrary neighborhood digraphs.     

Asymptotic inference for AR(1) processes with (nonnormal) stable errors

This is the first of several papers in which we consider problems related to the asymptotic distribution of the least squares estimate of the parameter γ in theAR(1) model $$X_k = \gamma X_{k - 1} + \varepsilon _k , k = 1,...,n,$$ where ε_k are independent identically distributed (i.i.d.) random variables in the domain of attraction of a stable law. In §1 we give a summary in the case ε_k is in the domain of attraction of the normal distribution. In §2 we consider errors in the domain of attraction of a (nonnormal) stable distribution. In §3 we prove a result in the case of the completely asymmetric stable distribution with α=β=1.     

Local robustness of sign tests in AR(1) against outliers

The paper deals with robustness of nonparametric sign tests against outliers in the autoregression AR(1) model. We consider the local scheme of data contamination by independent additive outliers with intensity O(n ^?1/2). The qualitative robustness of tests in terms of power equicontinuity is obtained.     

具有AR(1)误差的均值漂移模型的Score检验和似然比检验

讨论了具有AR(1)误差的线性均值漂移模型,研究了自相关性的检验问题,导出了关于误差相关性的Score检验统计量和似然比检验统计量,并把它推广到误差项为AR(1)非线性均值漂移模型.本文还给出了一个数值例子说明检验方法的实用性.