Tests of Parameters Instability: Theoretical Study and Empirical Applications on Two Types of Models (ARMA Model and Market Model)

This paper considers tests of parameters instability and structural change with known, unknown or multiple breakpoints. The results apply to a wide class of parametric models that are suitable for estimation by strong rules for detecting the number of breaks in a time series. For that, we use Chow, CUSUM, CUSUM of squares, Wald, likelihood ratio and Lagrange multiplier tests. Each test implicitly uses an estimate of a change point. We conclude with an empirical analysis on two different models (ARMA model and simple linear regression model).