Testing for structural breaks in GARCH models

Abstract

We study the ability of traditional diagnostic tests and LM and CUSUM structural break tests to detect a range of different types of breaks in GARCH models. We find that Wooldridge's (1990) robust LM tests for autocorrelation and ARCH have no power to detect structural breaks in GARCH models. However, CUSUM- and LM-based structural break tests have excellent size when the data is Gaussian, but the CUSUM tests tend to overreject even in quite large samples when returns have fat tails. However, the LM-based tests have approximately the correct size and exhibit impressive power to detect a range of breaks in the dynamics of conditional volatility. We apply these tests to a range of financial time series using returns starting only in 1990 and find that many GARCH models that pass standard specification tests fail the structural break tests.

Acknowledgements

I thank Adlai Fisher, an anonymous referee and participants at the 2003 Northern Finance Association meeting in Quebec city, and the 24th International Symposium of Forecasting in Sydney Australia for their comments. I also thank Kyung Shim for his research assistance. Any remaining errors are my own responsibility.

Notes

¹ The miss-specification indicator variable will generally be a function of the mean parameters θ_μ and possibly a nuisance parameter ξ: λ_t (θ_μ , ξ). The asymptotic distribution of the test statistics requires a -consistent estimator of this nuisance parameter .

² The results are similar when including only one lag.

³ Note that the IT test on raw returns also rejected too frequently.

⁴ The critical values 1.22, 1.36 and 1.63 are at 10, 5 and 1%, respectively.

⁵ I thank an anonymous referee for suggesting this experiment.

⁶ We have also considered results for longer sample periods dating back to July 1963 for the stock returns and 1974 for the foreign exchange rates. The full sample period results are much the same as our post-1989 data and are available on request. It should be no surprise that the evidence of structural breaks that we document for the post-1989 samples is much stronger in the longer sample.