Large sample inference based on multiple observations from nonlinear autoregressive processes
type: Item
instance of: scholarly article
title: Large sample inference based on multiple observations from nonlinear autoregressive processes
zbMATH Open document ID: 0796.62074
DOI: 10.1016/0304-4149(93)00068-Q
published in: Stochastic Processes and their Applications
publication date: 1994-03-27T00:00:00Z
review text: Let \(\{Y_ t(i) \mid t = 1,\dots,n\}\) be a time series for individual \(i\), \(i = 1,\dots,m\). The nonlinear autoregressive model \(Y_ t(i) = H(Y_{t - 1}(i); \theta_ i) + \varepsilon_ t(i)\) is considered, where the \(\theta_ i\)'s are \(p \times 1\) vectors of unknown parameters, \(H(y;\theta)\) is a known function and \(\varepsilon_ t(i)\) is a sequence of iid random variables for each \(i\). In section 2 of the paper the case ``\(n \to \infty\), \(m\) fixed'' is dealt with. The Wald statistic based on an asymptotically optimal one-step maximum likelihood estimator is proposed for testing the hypothesis \(H_ 0 : \theta_ 1 = \dots \theta_ m\). The null and non-null limiting distributions are deduced from the LAN property. Section 3 studies a special threshold autoregressive model of order 1 for the case ``\(n\) fixed, \(m \to \infty\)''. This section is mainly concerned with the derivation of the least squares estimator of the parameter vector and its limiting distribution. Section 4 discusses briefly some related topics.
Mathematics Subject Classification ID: 62M10
Mathematics Subject Classification ID: 62F05
Mathematics Subject Classification ID: 62E20
zbMATH DE Number: 513272
zbMATH Keywords: time series
zbMATH Keywords: nonlinear autoregressive model
zbMATH Keywords: Wald statistic
zbMATH Keywords: asymptotically optimal one-step maximum likelihood estimator
zbMATH Keywords: limiting distributions
zbMATH Keywords: LAN property
zbMATH Keywords: threshold autoregressive model of order 1
zbMATH Keywords: least squares estimator
author: S. Y. Hwang
author: I. V. Basawa
reviewed by: Rainer Schlittgen
MaRDI profile type: Publication
cites work: Statistics for Modern Business Decisions (2nd ed.).
cites work: Large-sample inference for a regression model with autocorrelated errors
cites work: Asymptotic optimal inference for non-ergodic models
cites work: Large-sample tests of homogeneity for time series models
cites work: Q4183968
cites work: On Large-Sample Estimation and Testing in Parametric Models
cites work: Asymptotic optimal inference for a class of nonlinear time series models
cites work: Local Asymptotic Normality for Non-Identically Distributed Observations
cites work: Q3672893
cites work: A threshold AR(1) model
cites work: Q4839937
cites work: Estimation in nonlinear time series models
cites work: Threshold models in non-linear time series analysis
cites work: Q3999154
description: scientific article; zbMATH DE number 513272