Mathematical Methods of Statistics

, Volume 27, Issue 2, pp 119–144 | Cite as

A Test of Correlation in the Random Coefficients of an Autoregressive Process

  • F. ProïaEmail author
  • M. Soltane


A random coefficient autoregressive process in which the coefficients are correlated is investigated. 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 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 in the random coefficients is violated. Finally, a consistent estimation is given together with a testing procedure for the existence of correlation in the coefficients. While convergence properties rely on ergodicity, we use a martingale approach to reach most of the results.


RCAR process,MAprocess random coefficients least squares estimation stationarity ergodicity symptotic normality autocorrelation 

2010 Mathematics Subject Classification

62M10 62F03 62F12 60G42 


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© Allerton Press, Inc. 2018

Authors and Affiliations

  1. 1.Laboratoire Angevin de Recherche en Math. (LAREMA), CNRSUniv. d’Angers, Univ. Bretagne LoireAngersFrance
  2. 2.Laboratoire Manceau de Math.Le Mans Univ.Le MansFrance

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