Long-Range Dependent Time Series Specification

Abstract

In this paper we propose using a nonparametric model specification test for parametric time series with long-range dependence (LRD). In order to establish asymptotic distributions of the proposed test statistic, we develop new central limit theorems for certain weighted quadratic forms of stationary time series with LRD. In order to implement the proposed test in practice, we develop a computer-intensive parametric bootstrap simulation procedure for finding simulated critical values. As a result, our finite-sample studies show that both the proposed theory and the simulation procedure work well and that the proposed test has little size distortion and reasonable power.

Keywords: Central limit theorem, Gaussian process, linear process, long-range dependence, parametric time series regression, specification testing

JEL Classification: C14, C32