Parametric inference in stationary time series models with dependent errors

Research output: Contribution to journalArticlepeer-review

Abstract

This article is concerned with inference for the parameter vector in stationary time series models based on the frequency domain maximum likelihood estimator. The traditional method consistently estimates the asymptotic covariance matrix of the parameter estimator and usually assumes the independence of the innovation process. For dependent innovations, the asymptotic covariance matrix of the estimator depends on the fourth-order cumulants of the unobserved innovation process, a consistent estimation of which is a difficult task. In this article, we propose a novel self-normalization-based approach to constructing a confidence region for the parameter vector in such models. The proposed procedure involves no smoothing parameter, and is widely applicable to a large class of long/short memory time series models with weakly dependent innovations. In simulation studies, we demonstrate favourable finite sample performance of our method in comparison with the traditional method and a residual block bootstrap approach.

Original languageEnglish (US)
Pages (from-to)772-783
Number of pages12
JournalScandinavian Journal of Statistics
Volume39
Issue number4
DOIs
StatePublished - Dec 2012

Keywords

  • Block bootstrap
  • Confidence region
  • Frequency domain
  • Long memory time series
  • Self-normalization

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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