Template-Type: ReDIF-Paper 1.0

Author-Name: Ai Deng
Author-X-Name-First: Ai
Author-X-Name-Last: Deng
Author-Email: dengai@bu.edu
Author-Workplace-Name: Department of Economics, Boston University

Author-Name: Pierre Perron
Author-X-Name-First: Pierre
Author-X-Name-Last: Perron
Author-Email: perron@bu.edu
Author-Workplace-Name: Department of Economics, Boston University


Title: A Non-local Perspective on the Power
Properties of the CUSUM and CUSUM of
Squares Tests for Structural Change

Abstract: We consider the power properties of the CUSUM and CUSUM of squares tests in
the presence of a one-time change in the parameters of a linear regression model. A
result due to Ploberger and Krämer (1990) is that the CUSUM of squares test has only
trivial asymptotic local power in this case, while the CUSUM test has non-trivial local
asymptotic power unless the change is orthogonal to the mean regressor. We argue that
such conclusions obtained from a local asymptotic framework are not reliable guides
to what happens in finite samples. The approach we take is to derive expansions of
the test statistics to order Op(T 1/2) that retain terms related to the magnitude of the
change under the alternative hypothesis. This enables us to analyze what happens for
non-local to zero breaks. Our theoretical results are able to explain how the power
function of the tests can be drastically different depending on whether one deals with
a static regression with uncorrelated errors, a static regression with correlated errors,
a dynamic regression with lagged dependent variables, or whether a correction for
non-Normality is applied in the case of the CUSUM of squares. We discuss in which
cases the tests are subject to a non-monotonic power function that goes to zero as the
magnitude of the change increases, and uncover some curious properties. All theoretical
results are verified to yield good guides to the finite sample power through simulation
experiments. We finally highlight the practical importance of our results.


Length: 38 pages
Creation-Date: 2005-11
Revision-Date: 
Publication-Status:
File-URL: http://people.bu.edu/perron/papers/cusum.pdf
File-Format: Application/pdf
File-Function: 
Number: WP2005-047
Classification-JEL:
Keywords: Change-point, Mean shift, Local asymptotic power, Recursive residuals,
Dynamic models
Handle: RePEc:bos:wpaper:WP2005-047