Parametric Inference in Stationary Time Series Models with Dependent Errors


Xiaofeng Shao, Department of Statistics, University of Illinois at Urbana-Champaign, 725 South Wright St, Champaign, IL 61820, USA.


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.