Large sample estimation in nonstationary autoregressive processes with multiple observations
type: Item
instance of: scholarly article
title: Large sample estimation in nonstationary autoregressive processes with multiple observations
zbMATH Open document ID: 0814.60028
DOI: 10.1016/0304-4149(94)00024-7
author: Sankara N. Sethuraman
author: I. V. Basawa
published in: Stochastic Processes and their Applications
publication date: 1995-06-13T00:00:00Z
review text: Let \(Z_ t = (Z_{t1}, \dots, Z_{tn})^ T\) denote an \((n \times 1)\) vector of observations at time \(t=1, \dots, m\). Suppose that \(\{Z_ t\}\) satisfies the autoregressive difference equation \(Z_ t = \sum^ p_{i=1} \theta_ i Z_{t-i} + \xi_ t\), \(t = 0, \pm 1, \pm 2, \dots\). The asymptotic distributions of the least-squares estimations of the parameters are derived both when \(m \to \infty\) and \(n \to \infty\) for the two nonstationary cases, viz., (a) the explosive case and (b) the unstable case. Consequently, the authors investigate the two-dimensional process \(Z_{ts} = \sum^ p_{i=1} \theta_ i Z_{t-i,s} + \xi_{ts}\), \(t,s = 0, \pm 1, \pm 2, \dots\). Nonstandard limit distributions are obtained.
Mathematics Subject Classification ID: 60F99
Mathematics Subject Classification ID: 60G12
Mathematics Subject Classification ID: 62F10
zbMATH DE Number: 724751
zbMATH Keywords: explosive process
zbMATH Keywords: unstable process
zbMATH Keywords: nonstandard limit distributions
zbMATH Keywords: asymptotic distributions of the least-squares estimations
zbMATH Keywords: nonstationary cases
reviewed by: Zhengyan Lin
MaRDI profile type: Publication
full work available at URL: 0304-4149(94)00024-7
OpenAlex ID: W2026575306
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description: scientific article; zbMATH DE number 724751