Bootstrapping Periodic State-Space Models

This article is concerned with how the bootstrap can be applied to study conditional forecast error distributions and construct prediction regions for future observations in periodic time-varying state-space models. We derive, first, an algorithm for assessing the precision of quasi-maximum likelihood estimates of the parameters. As a result, the derived algorithm is exploited for numerically evaluating the conditional forecast accuracy of a periodic time series model expressed in state space form. We propose a method which requires the backward, or reverse-time, representation of the model for assessing conditional forecast errors. Finally, the small sample properties of the proposed procedures will be investigated by some simulation studies. Furthermore, we illustrate the results by applying the proposed method to a real time series.     

A Bayesian analysis of a change in the parameters of autoregressive time series

In this article, we consider a Bayesian analysis of a possible change in the parameters of autoregressive time series of known order p, AR(p). An unconditional Bayesian test based on highest posterior density (HPD) credible sets is determined. The test is useful to detect a change in any one of the parameters separately. Using the Gibbs sampler algorithm, we approximate the posterior densities of the change point and other parameters to calculate the p-values that define our test.     

Predictive Density Order Selection of Periodic AR Models

This article considers the order selection problem of periodic autoregressive models. Our main goal is the adaptation of the Bayesian Predictive Density Criterion (PDC), established by Djuric' and Kay (1992 Djuric' , P. M. , Kay , S. M. ( 1992 ). Order selection of autoregressive models . IEEE Transactions on Signal Processing 40 : 2829 – 2833 . [Google Scholar]) for selecting the order of a stationary autoreg-ressive model, to deal with the order identification problem of a periodic autoregressive model. The performance of the established criterion, (P-PDC), is compared, via simulation studies, to the performances of some well-known existing criteria.     

Performance measures of M/G/1 retrial queues with recurrent customers,breakdowns, and general delays

In this paper, an M/G/1 retrial system with two classes of customers: transit and recurrent customers is studied. After service completion, recurrent customers always return to the orbit and transit customers leave the system forever. The server is subject to breakdowns and delayed repairs. The customer whose service is interrupted stays in the service, waiting for delay and repair of the server. After repair this customer completes his service. The study of the system concerns the joint generating function of the server state and the queue length in steady state. Some performance measures of the system are then derived and some numerical results are presented to illustrate the effect of the system parameters on the developed performance measures.     

Power periodic threshold GARCH model: Structure and estimation

Abstract

In this paper, we introduce and study the Power Periodic Threshold GARCH Model (PPTGARCH). We give the necessary and sufficient conditions for the existence of the unique strictly periodically stationary solution of the model and the necessary and sufficient conditions for the existence of moments. A sufficient condition for the periodic geometric ergodicity and β – mixing property using the uniform countable additivity condition is given. We prove the consistency and asymptotic normality of the Quasi-Maximum Likelihood estimator (QMLE) of the parameters. Simulation studies to illustrate consistency and asymptotic normality of the estimators for different underlying error distributions are presented.     

The analysis of unreliable M[X]/G/1 queuing system with loss,vacation and two delays of verification

This paper considers an M^[X]/G/1 queue with breakdowns, repair, Bernoulli vacation, two delays and geometric loss. In this paper, a special attention is given to the limiting distribution of system states. We obtain simplified expressions for the Probability Generating Functions (PGFs) of the joint distribution of server state and system size. Some performance measures were derived from the analysis of the steady state probabilities. PGF of a departure point system size distribution is developed. Particular cases of the studied system were investigated. The effect of system parameters on the main performance measures are illustrated and discussed.     

Recursive Estimation of GARCH Models

This article develops three recursive on-line algorithms, based on a two-stage least squares scheme for estimating generalized autoregressive conditionally heteroskedastic (GARCH) models. The first one, denoted by 2S-RLS, is an adaptation of the recursive least squares method for estimating autoregressive conditionally heteroskedastic (ARCH) models. The second and the third ones (denoted, respectively, by 2S-PLR and 2S-RML) are adapted versions of the pseudolinear regression (PLR) and the recursive maximum likelihood (RML) methods to the GARCH case. We show that the proposed algorithms give consistent estimators and that the 2S-RLS and the 2S-RML estimators are asymptotically Gaussian. These methods seem very adequate for modeling the sequential feature of financial time series, which are observed on a high-frequency basis. The performance of these algorithms is shown via a simulation study.     

Chi-Squared Type Test for the AFT-Generalized Inverse Weibull Distribution

The generalized inverse Weibull distribution is a newlife time probability distribution which can be used to model a variety of failure characteristics. It has several desirable properties and nice physical interpretations which enable them to be used frequently. In this article, we present a chi-squared goodness-of-fit test for an accelerated failure time (AFT) model with generalized inverse Weibull distribution (GIW) as the baseline distribution, in both of complete and censored data. This test is based on a modification of the NRR (Nikulin-Rao-Robson) statistic Y², proposed by Bagdonavicius and Nikulin (2011 Bagdonavicius, V., Nikulin, M. (2011). Chi-squared tests for general composite hypotheses from censored samples. Comptes Rendus Mathematique, Ser. I, 349(3–4): 219–223.[Crossref], [Web of Science ®] , [Google Scholar]), for censored data. Two applications of real data are given to illustrate the potentiality of the proposed test.