Statistica Sinica 15(2005), 795-817

MODEL DIAGNOSIS FOR SETAR TIME SERIES

Hira L. Koul$^1$, Winfried Stute$^2$ and Fang Li$^1$

$^1$Michigan State University and $^2$University of Giessen

Abstract: This paper discusses asymptotically distribution free (ADF) tests in self-exciting threshold autoregressive (SETAR) models. We also consider the case when the two different line segments have no jump. These tests are based on a marked empirical process of the underlying residuals. The paper also discusses the asymptotic behavior of the residual empirical process and ADF tests for the error distribution. We find that under some mild conditions, the asymptotic null behavior of both of these processes does not depend on the preliminary estimator of the change point parameter. Moreover, somewhat surprisingly, the asymptotic behavior of the residual empirical process in these models is the same as in the one-sample location model, as long as the residuals are based on an asymptotically linear estimator of the line segment parameters. The paper also includes a simulation study analyzing the finite sample behavior of some of the proposed tests.

Key words and phrases: Marked point processes, martingale type transform, model checks, time series.