The Experts below are selected from a list of 291 Experts worldwide ranked by ideXlab platform
Frédéric Proïa - One of the best experts on this subject based on the ideXlab platform.
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Testing for residual correlation of any order in the Autoregressive Process
Communications in Statistics - Theory and Methods, 2018Co-Authors: Frédéric ProïaAbstract:We are interested in the implications of a linearly autocorrelated driven noise on the asymptotic behavior of the usual least squares estimator in a stable Autoregressive Process. We show that the least squares estimator is not consistent and we suggest a sharp analysis of its almost sure limiting value as well as its asymptotic normality. We also establish the almost sure convergence and the asymptotic normality of the estimated serial correlation parameter of the driven noise. Then, we derive a statistical procedure enabling to test for correlation of any order in the residuals of an Autoregressive modelling, giving clearly better results than the commonly used portmanteau tests of Ljung-Box and Box-Pierce, and appearing to outperform the Breusch-Godfrey procedure on small-sized samples.
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A test of correlation in the random coefficients of an Autoregressive Process
Mathematical Methods of Statistics, 2018Co-Authors: Frédéric Proïa, Marius SoltaneAbstract:A random coefficient Autoregressive Process is deeply investigated in which the coefficients are correlated. First we look at the existence of a strictly stationary causal solution, then we give the second-order stationarity conditions and the autocorrelation function of the Process. Then we study some asymptotic properties of the empirical mean and the usual least squares estimators of the Process, such as convergence, asymptotic normality and rates of convergence, supplied with the appropriate assumptions on the driving perturbations. Our objective is to get an overview of the influence of correlated coefficients in the estimation step, through a simple model. In particular, the lack of consistency is shown for the estimation of the Autoregressive parameter. Finally, a consistent estimation is given together with a testing procedure for the existence of correlation in the random coefficients. While convergence properties rely on the ergodicity, we use a martingale approach to reach most of the results.
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A test of correlation in the random coefficients of an Autoregressive Process
arXiv: Statistics Theory, 2016Co-Authors: Frédéric Proïa, Marius SoltaneAbstract:A random coefficient Autoregressive Process is deeply investigated in which the coefficients are correlated. First we look at the existence of a strictly stationary causal solution, we give the second-order stationarity conditions and the autocorrelation function of the Process. Then we study some asymptotic properties of the empirical mean and the usual estimators of the Process, such as convergence, asymptotic normality and rates of convergence, supplied with the appropriate assumptions on the driving perturbations. Our objective is to get an overview of the influence of correlated coefficients in the estimation step, through a simple model. In particular, the lack of consistency is shown for the estimation of the Autoregressive parameter when the independence hypothesis is violated in the random coefficients. Finally, a consistent estimation is given together with a testing procedure for the existence of correlation in the coefficients. While convergence properties rely on the ergodicity, we use a martingale approach to reach most of the results.
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A sharp analysis on the asymptotic behavior of the Durbin-Watson statistic for the first-order Autoregressive Process
ESAIM: Probability and Statistics, 2013Co-Authors: Bernard Bercu, Frédéric ProïaAbstract:The purpose of this paper is to provide a sharp analysis on the asymptotic behavior of the Durbin-Watson statistic. We focus our attention on the first-order Autoregressive Process where the driven noise is also given by a first-order Autoregressive Process. We establish the almost sure convergence and the asymptotic normality for both the least squares estimator of the unknown parameter of the Autoregressive Process as well as for the serial correlation estimator associated to the driven noise. In addition, the almost sure rates of convergence of our estimates are also provided. It allows us to establish the almost sure convergence and the asymptotic normality for the Durbin-Watson statistic. Finally, we propose a new bilateral statistical test for residual autocorrelation.
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Further results on the H-Test of Durbin for stable Autoregressive Processes
Journal of Multivariate Analysis, 2013Co-Authors: Frédéric ProïaAbstract:The purpose of this paper is to investigate the asymptotic behavior of the Durbin–Watson statistic for the stable p-order Autoregressive Process when the driven noise is given by a first-order Autoregressive Process. It is an extension of the previous work of Bercu and Proia devoted to the particular case p=1. We establish the almost sure convergence and the asymptotic normality for both the least squares estimator of the unknown vector parameter of the Autoregressive Process as well as for the serial correlation estimator associated with the driven noise. In addition, the almost sure rates of convergence of our estimates are also provided. Then, we prove the almost sure convergence and the asymptotic normality for the Durbin–Watson statistic and we derive a two-sided statistical procedure for testing the presence of a significant first-order residual autocorrelation that appears to simplify and to improve the well-known h-test suggested by Durbin. Finally, we briefly summarize our observations on simulated samples.
Marius Soltane - One of the best experts on this subject based on the ideXlab platform.
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ASYMPTOTIC EFFICIENCY IN THE Autoregressive Process DRIVEN BY A STATIONARY GAUSSIAN NOISE
arXiv: Statistics Theory, 2018Co-Authors: Marius SoltaneAbstract:The first purpose of this article is to obtain a.s. asymptotic properties of the maximum likelihood estimator in the Autoregressive Process driven by a stationary Gaussian noise. The second purpose is to show the local asymptotic normality property of the likelihoods ratio in order to get a notion of asymptotic efficiency and to build an asymptotically uniformly invariant most powerful procedure for testing the significance of the Autoregressive parameter.
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A test of correlation in the random coefficients of an Autoregressive Process
Mathematical Methods of Statistics, 2018Co-Authors: Frédéric Proïa, Marius SoltaneAbstract:A random coefficient Autoregressive Process is deeply investigated in which the coefficients are correlated. First we look at the existence of a strictly stationary causal solution, then we give the second-order stationarity conditions and the autocorrelation function of the Process. Then we study some asymptotic properties of the empirical mean and the usual least squares estimators of the Process, such as convergence, asymptotic normality and rates of convergence, supplied with the appropriate assumptions on the driving perturbations. Our objective is to get an overview of the influence of correlated coefficients in the estimation step, through a simple model. In particular, the lack of consistency is shown for the estimation of the Autoregressive parameter. Finally, a consistent estimation is given together with a testing procedure for the existence of correlation in the random coefficients. While convergence properties rely on the ergodicity, we use a martingale approach to reach most of the results.
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A test of correlation in the random coefficients of an Autoregressive Process
arXiv: Statistics Theory, 2016Co-Authors: Frédéric Proïa, Marius SoltaneAbstract:A random coefficient Autoregressive Process is deeply investigated in which the coefficients are correlated. First we look at the existence of a strictly stationary causal solution, we give the second-order stationarity conditions and the autocorrelation function of the Process. Then we study some asymptotic properties of the empirical mean and the usual estimators of the Process, such as convergence, asymptotic normality and rates of convergence, supplied with the appropriate assumptions on the driving perturbations. Our objective is to get an overview of the influence of correlated coefficients in the estimation step, through a simple model. In particular, the lack of consistency is shown for the estimation of the Autoregressive parameter when the independence hypothesis is violated in the random coefficients. Finally, a consistent estimation is given together with a testing procedure for the existence of correlation in the coefficients. While convergence properties rely on the ergodicity, we use a martingale approach to reach most of the results.
Serguei Pergamenchtchikov - One of the best experts on this subject based on the ideXlab platform.
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the tail of the stationary distribution of a random coefficient ar q model
arXiv: Probability, 2004Co-Authors: Claudia Kluppelberg, Serguei PergamenchtchikovAbstract:We investigate a stationary random coefficient Autoregressive Process. Using renewal type arguments tailor-made for such Processes, we show that the stationary distribution has a power-law tail. When the model is normal, we show that the model is in distribution equivalent to an Autoregressive Process with ARCH errors. Hence, we obtain the tail behavior of any such model of arbitrary order.
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the tail of the stationary distribution of a random coefficient ar q model
Annals of Applied Probability, 2004Co-Authors: Claudia Kluppelberg, Serguei PergamenchtchikovAbstract:We investigate a stationary random cofficient Autoregressive Process. Using renewal type arguments tailor-made for such Processes we show that the stationary distribution has a power-law tail. When the model is normal, we show that the model is in distribution equivalent to an Autoregressive Process with ARCH errors. Hence we obtain the tail behaviour of any such model of arbitrary order.
Miroslav M. Ristić - One of the best experts on this subject based on the ideXlab platform.
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A Generalization to Bivariate Mittag–Leffler and Bivariate Discrete Mittag–Leffler Autoregressive Processes
Communications in Statistics - Theory and Methods, 2010Co-Authors: K. Jayakumar, Miroslav M. Ristić, Davis Antony MundasseryAbstract:A generalization of the Gaver and Lewis (1980) model of first-order Autoregressive Process with marginals as bivariate Mittag–Leffler distribution is obtained. A necessary and sufficient condition for stationarity of the Process is established. Autoregressive Process with marginals follow bivariate discrete Mittag–Leffler distribution is also developed. The unknown parameters of the Processes are estimated and some numerical results of the estimations are given.
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A Beta–Gamma Autoregressive Process of the second-order (BGAR(2))
Statistics & Probability Letters, 2005Co-Authors: Miroslav M. RistićAbstract:Abstract In this paper we present a stationary Beta–Gamma Autoregressive Process of the second-order which represents the generalization of the Beta–Gamma Autoregressive Process of the first-order [Lewis, McKenzie, Hugus, 1989. Comm. Statist. Stochastic Models 5, 1–30]. The defined Process has Gamma ( k , β ) marginally distributions. The properties of the Process are discussed. The conditional least-squares estimation and the method of moments are used. Asymptotic distributions of the estimates are given and the asymptotic confidence regions are obtained. Some numerical results of the estimations are given.
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A bivariate uniform Autoregressive Process
Annals of the Institute of Statistical Mathematics, 2003Co-Authors: Miroslav M. Ristić, Biljana Č. PopovićAbstract:We define the bivariate first order stationary Autoregressive Process {(X n ,Y n )} with uniform marginal distribution where {X n } and {Y n } are the two stationary sequences with uniformU(0, 1) marginal distributions. We also estimate the unknown parameters of the model.
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The uniform Autoregressive Process of the second order (UAR(2))
Statistics & Probability Letters, 2002Co-Authors: Miroslav M. Ristić, Biljana Č. PopovićAbstract:We introduce a stationary uniform Autoregressive Process of second order. Spectral density, autocovariance and autocorrelation functions are derived. The unknown parameters of this model are estimated by the conditional least squares.
S. Pergamenshchikov - One of the best experts on this subject based on the ideXlab platform.
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truncated sequential estimation of the parameter of a first order Autoregressive Process with dependent noises
Mathematical Methods of Statistics, 2009Co-Authors: D Fourdrinier, V. Konev, S. PergamenshchikovAbstract:For a first-order non-explosive Autoregressive Process with dependent noise, we propose a truncated sequential procedure with a fixed mean-square accuracy. The asymptotic distribution of the estimator depends on the type of the noise distribution: it is normal when the noise has a Kotz’s distribution, while it is a mixture of normal distributions if the noise distribution is a variance mixture of normal distrbutions as well. In both cases, the convergence to the limiting distribution is uniform in the unknown parameter.
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On guaranteed estimation of the mean of an Autoregressive Process
The Annals of Statistics, 1997Co-Authors: V. Konev, S. PergamenshchikovAbstract:This paper considers the problem of sequential point estimation of the mean of a stable Autoregressive Process with unknown scale and Autoregressive parameters. The construction ofa sequential procedure makes use of special stopping rules and some modifications of least-squares estimates. The procedure enables estimating the mean with prescribed mean-square accuracy uniformly in nuisance parameters. The uniform asymptotic normality and the asymptotic minimaxity of the sequential estimate are established. The asymptotic formula for the mean sample size is obtained.
