MONITORING STRUCTURAL CHANGES WITH THE GENERALIZED FLUCTUATION TEST

In this paper we introduce the generalized fluctuation test for monitoring structural changes and establish a result characterizing the limiting behavior of this class of tests. As applications of the generalized fluctuation test, tests based on the maximum and range of the fluctuation of moving estimates are proposed. We also derive the boundary functions for the proposed tests and tabulate simulated critical values. Our simulations indicate that these tests compare favorably with the recursive-estimates-based test considered by Chu, Stinchcombe, and White (1996, Econometrica 64, 1045–1065) when a change occurs late.

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

[2]  Ross Ihaka,et al.  Gentleman R: R: A language for data analysis and graphics , 1996 .

[3]  Chung-Ming Kuan.  Tests for changes in models with a polynomial trend , 1998 .

[4]  Herman J. Bierens.  Testing Parameter Constancy of Linear Regressions , 1984 .

[5]  J. Bai,et al.  Least squares estimation of a shift in linear processes , 1994 .

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

[7]  J. Bai,et al.  Least Absolute Deviation Estimation of a Shift , 1995, Econometric Theory.

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

[9]  R. Varga,et al.  Proof of Theorem 4 , 1983 .

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

[11]  H. Robbins,et al.  Boundary Crossing Probabilities for the Wiener Process and Sample Sums , 1970 .

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

[13]  P. Révész.  On the Increments of Wiener and Related Processes , 1982 .

[14]  H. Robbins.  Statistical Methods Related to the Law of the Iterated Logarithm , 1970 .

[15]  William Feller,et al.  An Introduction to Probability Theory and Its Applications , 1967 .

[16]  H. White,et al.  Monitoring Structural Change , 1996 .

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

[18]  P. Révész,et al.  Weak Laws for the Increments of Wiener Processes, Brownian Bridges Empirical Processes and Partial Sums of I.I.D.R.V.’S , 1987 .

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

[20]  P. Perron,et al.  Estimating and testing linear models with multiple structural changes , 1995 .

[21]  W. Krämer,et al.  Testing for structural change in dynamic models , 1988 .