Wald Tests for Detecting Multiple Structural Changes in Persistence

Abstract

This paper considers the problem of testing for multiple structural changes in the persistence of a univariate time series. We propose sup-Wald tests of the null hypothesis that the process is a unit root against the alternative hypothesis that the process alternates between stationary and unit root regimes. Both non-trending and trending cases are analyzed. We derive the limit distributions of the tests under the null and establish their consistency under the relevant alternatives. The computation of the test statistics as well as asymptotic critical values is facilitated by the dynamic programming algorithm proposed in Perron and Qu (2006) which allows the minimization of the sum of squared residuals under the alternative hypothesis while imposing within and cross regime restrictions on the parameters. Finally, we present Monte Carlo evidence to show that the proposed tests perform quite well in …nite samples relative to those that currently exist in the literature.

A Note on Estimating and Testing for Multiple Structural Changes in Models With Endogenous Regressors via 2sls

“…Perron and Qu (2006) extended the analysis to the case where linear restrictions are imposed on the coe¢ cients of the model and also considerably relaxed the assumptions used in Bai and Perron (1998). Recent contributions of interest include improved testing procedures to test for changes in a trend function allowing for a stationary or integrated noise component (Perron and Yabu, 2009, Harvey et al, 2011, Sayginsoy and Vogelsang, 2011, the ensuing development of tests for unit root allowing for a change in trend under both the null and alternative hypotheses , Carrion-i-Silvestre et al, 2009, Harris et al, 2009, as well as improvements related to testing for changes in persistence (Kejriwal et al, 2012).…”

Unit root tests

“…Kejriwal et al proposed hybrid testing procedures that allows ruling out of stable stationary processes or ones that are subject to only stationary changes under the null, helping the researcher in interpreting a rejection as emanating from a switch between an I (1) and an I (0) regime. The authors use a combination of their own developed URTs together with a test with a null of no breaks versus an alternative with one or more breaks given by Bai and Perron .…”

“…Kejriwal et al used the approach of detrending the data when trends are included prior to using their hybrid testing procedure and they suggest using a sequential procedure developed by Kejriwal et al that is robust to whether the errors are I (1) or I (0). The smallest time series length the authors consider is 150.…”

Nonparametric test for a constant beta between Itô semi-martingales based on high-frequency data

“…First, there is an enormous amount of literature on parameter shifts and breaks (Kejriwal et al, 2013, and references therein), but the results are all based on a long span ergodic-type theory rather than fixed length in-fill conducted here. Second, Ang and Kristensen (2012) propose a test for constant beta based on a Hausman type statistic that compares a nonparametric kernel-based estimate of betas at fixed time points and a long-run estimate of beta.…”