Tests for changes in models with a polynomial trend

Abstract In this paper, we propose a class of tests for changes in models with a polynomial trend, based on the ‘generalized fluctuation’ testing principle of Kuan and Hornik (1995). We derive the asymptotic null distributions of the proposed tests and tabulate their asymptotic critical values. We also show that these tests are consistent and have non-trivial local power against a wide class of alternatives. The simulation results suggest that the proposed tests can complement the existing tests in different time trend models.

[1]  D. Andrews.  Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation , 1991 .

[2]  W. Krämer,et al.  A new test for structural stability in the linear regression model , 1989 .

[3]  Ian B. MacNeill,et al.  Properties of Sequences of Partial Sums of Polynomial Regression Residuals with Applications to Tests for Change of Regression at Unknown Times , 1978 .

[4]  J. Bai,et al.  Testing for Parameter Constancy in Linear Regressions: An Empirical Distribution Function Approach , 1996 .

[5]  K. Hornik,et al.  The Moving-Estimates Test for Parameter Stability , 1995, Econometric Theory.

[6]  D. Andrews,et al.  Further Evidence on the Great Crash, the Oil-Price Shock, and the Unit-Root Hypothesis , 1992 .

[7]  J. Durbin,et al.  Techniques for Testing the Constancy of Regression Relationships Over Time , 1975 .

[8]  J. Stock,et al.  Recursive and Sequential Tests of the Unit Root and Trend Break Hypothesis: Theory and International Evidence , 1990 .

[9]  W. Newey,et al.  A Simple, Positive Semi-Definite, Heteroskedasticity and Autocorrelationconsistent Covariance Matrix , 1986 .

[10]  K. Hornik,et al.  Mosum Tests for Parameter Constancy , 1995 .

[11]  Chia-Shang James Chu,et al.  A Direct Test for Changing Trend , 1992 .

[12]  D. Andrews,et al.  Optimal Tests When a Nuisance Parameter Is Present Only Under the Alternative , 1992 .

[13]  P. Perron,et al.  The Great Crash, The Oil Price Shock And The Unit Root Hypothesis , 1989 .

[14]  Peter Hackl,et al.  The Use of MOSUMS for Quality Control , 1978 .

[15]  D. Andrews.  Tests for Parameter Instability and Structural Change with Unknown Change Point , 1993 .

[16]  K. Hornik,et al.  The generalized fluctuation test: A unifying view , 1995 .

[17]  Walter Krämer,et al.  The CUSUM test for OLS residuals , 1992 .

[18]  Pranab Kumar Sen.  Asymptotic theory of some tests for a possible change in the regression slope occurring at an unknown time point , 1980 .

[19]  Jeffrey M. Wooldridge,et al.  Some Invariance Principles and Central Limit Theorems for Dependent Heterogeneous Processes , 1988, Econometric Theory.