A class of time-reversible semi-Markov processes

In this paper, we investigate a class of semi-Markov processes, first touched upon lightly in Pyke and Schaufele (1966), that are time-reversible. Results that are difficult to prove for semi-Markov processes in general are often made more simple for time-reversible semi-Markov processes, and some examples are given.     

A BINAR(1) time-series model with cross-correlated COM–Poisson innovations

This article proposes a bivariate integer-valued autoregressive time-series model of order 1 (BINAR(1) with COM–Poisson marginals to analyze a pair of non stationary time series of counts. The interrelation between the series is induced by the correlated innovations, while the non stationarity is captured through a common set of time-dependent covariates that influence the count responses. The regression and dependence effects are estimated using generalized quasi-likelihood (GQL) approach. Simulation experiments are performed to assess the performance of the estimation algorithms. The proposed BINAR(1) process is applied to analyze a real-life series of day and night accidents in Mauritius.     

Spurious Instrumental Variables

Spurious regression phenomenon has been recognized for a wide range of Data Generating Processes: driftless unit roots, unit roots with drift, long memory, trend and broken-trend stationarity, etc. The usual framework is Ordinary Least Squares. We show that the spurious phenomenon also occurs in Instrumental Variables estimation when using non stationary variables, whether the non stationarity component is stochastic or deterministic. Finite sample evidence supports the asymptotic results.     

时间序列平稳性分析的自动机制研究

平稳性分析是建立时间序列自回归滑动平均模型的一个预处理过程,已有的分析方法研究颇多,但尚缺乏一个自动判定平稳性的机制。文章在分析自相关函数的基础上,引入非线性转换理论进行改进,并采用聚类方法建立时间序列平稳性分析的自动机制,为大批量时间序列的平稳性自动判定提供了一条新途径。文中采用了一组模拟数据和一组金融数据来进行实证分析,实验表明,平稳性分析的自动机制能得到较好的结果。     

Non-stationary structural model with time-varying demand elasticities

The paper considers local linear regression of a time series model with non-stationary regressors and errors. Asymptotic property of the local linear estimator is derived under a new dependence measure of non-stationary time series. We apply the local linear regression method to estimate the “time-varying” coefficients of an economic-causal model for the industrial sector of the U.S. economy. Nonparametric bootstrap test on the time-varying coefficients strongly suggests that the price/income elasticities of the U.S. durable goods demand are time-varying.     

Weak approximations for quantile processes of stationary sequences

ABSTRACT By studying the deviations between uniform empirical and quantile processes (the so-called Bahadur-Kiefer representations) of a stationary sequence in properly weighted sup-norm metrics, we find a general approach to obtaining weighted results for uniform quantile processes of stationary sequences. Consequently we are able to obtain weak convergence for weighted uniform quantile processes of stationary mixing and associated sequences. Further, by studying the sup-norm distance of a general quantile process from its corresponding uniform quantile process, we find that information at the two end points of the uniform quantile process can be so utilized that this weighted sup-norm distance converges in probability to zero under the so-called Csörgõ-Révész conditions. This enables us to obtain weak convergence for weighted general quantile processes of stationary mixing and associated sequences.     

Measuring serial dependence in categorical time series

The analysis of time-indexed categorical data is important in many fields, e.g., in telecommunication network monitoring, manufacturing process control, ecology, etc. Primary interest is in detecting and measuring serial associations and dependencies in such data. For cardinal time series analysis, autocorrelation is a convenient and informative measure of serial association. Yet, for categorical time series analysis an analogous convenient measure and corresponding concepts of weak stationarity have not been provided. For two categorical variables, several ways of measuring association have been suggested. This paper reviews such measures and investigates their properties in a serial context. We discuss concepts of weak stationarity of a categorical time series, in particular of stationarity in association measures. Serial association and weak stationarity are studied in the class of discrete ARMA processes introduced by Jacobs and Lewis (J. Time Ser. Anal. 4(1):19–36, 1983). An intrinsic feature of a time series is that, typically, adjacent observations are dependent. The nature of this dependence among observations of a time series is of considerable practical interest. Time series analysis is concerned with techniques for the analysis of this dependence. (Box et al. 1994p. 1)     

C219. Comment on ”calculating binomial probabilities when the trial probabilities are unequal“

In complex models like hidden Markov chains, the convergence of the MCMC algorithms used to approximate the posterior distribution and the Bayes estimates of the parameters of interest must be controlled in a robust manner. We propose in this paper a series of online controls, which rely on classical non-parametric tests, to evaluate independence from the start-up distribution, stability of the Markov chain, and asymptotic normality. These tests lead to graphical control spreadsheets which arepresentedin the set-up of normalmixture hidden Markov chains to compare the full Gibbs sampler with an aggregated Gibbs sampler based on the forward – backward formulas.     

Bayesian spatio‐temporal models based on discrete convolutions

Abstract: The authors consider a class of models for spatio‐temporal processes based on convolving independent processes with a discrete kernel that is represented by a lower triangular matrix. They study two families of models. In the first one, spatial Gaussian processes with isotropic correlations are convoluted with a kernel that provides temporal dependencies. In the second family, AR(p) processes are convoluted with a kernel providing spatial interactions. The covariance structures associated with these two families are quite rich. Their covariance functions that are stationary and separable in space and time as well as time dependent nonseparable and nonisotropic ones.     

Large deviations of multiclass M/G/1 queues

Consider a multiclass M/G/1 queue where queued customers are served in their order of arrival at a rate which depends on the customer class. We model this system using a chain with states represented by a tree. Since the service time distribution depends on the customer class, the stationary distribution is not of product form so there is no simple expression for the stationary distribution. Nevertheless, we can find a harmonic function on this chain which provides information about the asymptotics of this stationary distribution. The associated h‐transformation produces a change of measure that increases the arrival rate of customers and decreases the departure rate thus making large deviations common. The Canadian Journal of Statistics 37: 327–346; 2009 © 2009 Statistical Society of Canada