Computationally attractive stability tests for the efficient method of moments

This paper develops structural stability tests based on the Efficient Method of Moments for the case of a known breakpoint. Computationally attractive post-sample estimators and test-statistics for structural stability are proposed, which are modifications of the Lagrange Multiplier, Likelihood Ratio, Wald and Hansen tests for structural stability. The modifications retain the asymptotic optimality properties against certain local alternatives of those based on efficient computationally intensive estimators for the post-sample data. Evaluation of these tests is performed in the context of stochastic volatility models. For these types of models and datasets, readily available structural stability tests are important as these models are used in the pricing of options where the arrival of new data constantly raises the issue of whether the estimates are in need of updating. A Monte Carlo study gives encouraging results for the computationally attractive tests. An application is made to stochastic volatility models for daily returns of the S&P500 index ranging from 1981 to 1993. The tests do not reject the null hypothesis of structural stability for the final model.