On limiting distributions in explosive autoregressive processes
type: Item
instance of: scholarly article
title: On limiting distributions in explosive autoregressive processes
zbMATH Open document ID: 0909.62011
DOI: 10.1016/S0167-7152(97)00111-9
author: Michael J. Monsour
author: Piotr W. Mikulski
published in: Statistics \& Probability Letters
publication date: 1999-04-08T00:00:00Z
review text: Let \[ Y_n= \beta'\widetilde{Y}_{n-1}+ \varepsilon_n, \quad\varepsilon_n\text{ i.i.d. } N(0,1), \quad n=1,2,\dots \] be the \(p\) th order purely explosive autoregressive process where \(\beta= (\beta_1,\dots, \beta_p)'\) is a real \(p\)-vector, which is unknown and \(\widetilde{Y}_j= (Y_j,\dots, Y_{j-p+1})'\). Let \(A_n= \sum_{j=1}^n \widetilde{Y}_{j-1} \widetilde{Y}_{j-1}'\). Then, the maximum likelihood estimator \(\widehat{\beta}_n\) is given by \[ \widehat{\beta}_n= A_n^{-1} \sum_{j=1}^n \widetilde{Y}_{j-1} \widetilde{Y}_j'. \] The limiting distributions of \(\widehat{\beta}_n\) (with a random or nonrandom normalization) are known, but the detailed proofs have been omitted in the literature. The author gives detailed proofs for these results.
Mathematics Subject Classification ID: 62E20
Mathematics Subject Classification ID: 62M10
zbMATH DE Number: 1124489
zbMATH Keywords: characteristic roots
zbMATH Keywords: Jordan normal
zbMATH Keywords: canonical form
zbMATH Keywords: pure explosive autoregressive process
reviewed by: Ken-ichi Yoshihara
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1124489