Testing for Structural Stability in the Whole Sample

The paper examines a Lagrange Multiplier type test for the constancy of the parameter in general models with dependent data without imposing any arti…cial choice of the possible location of the break. In order to prove the asymptotic behaviour of the test, we extend a strong approximation result for partial sums of a sequence of random variables. We also present a Monte-Carlo experiment to examine the …nite sample performance of the test and how it compares with tests which assume some knowledge of the possible location of the break.