 THE DISTRIBUTION OF NONSTATIONARY AUTOREGRESSIVE PROCESSES UNDER GENERAL NOISE CONDITIONSJames C. Spall Journal of Time Series Analysis, 1993, vol. 14, issue 3, 317-330 Abstract: Abstract. In this paper we consider the long‐run distribution of a multivariate autoregressive process of the form xn=An‐1xn‐1+ noise, where the noise has an unknown (possibly nonstationary and nonindependent) distribution and An is a (generally) time‐varying transition matrix. It can easily be shown that the process xn need not have a known long‐run distribution (in particular, central limit theorem effects do not generally hold). However, if the distribution of the noise approaches a known distribution as n gets large, we show that the distribution of xn may also approach a known distribution for large n. Such a setting might occur, for example, when transient effects associated with the early stages of a system's operation die out. We first present a general result that applies for arbitrary noise distributions and general An. Several special cases are then presented that apply for noise distributions in the infinitely divisible class and/or for asymptotically constant coefficient An. We illustrate the results on a problem in characterizing the asymptotic distribution of the estimation error in a Kalman filter. Date: 1993 Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:bla:jtsera:v:14:y:1993:i:3:p:317-330 Ordering information: This journal article can be ordered from Access Statistics for this article Journal of Time Series Analysis is currently edited by M.B. Priestley More articles in Journal of Time Series Analysis from Wiley Blackwell |
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