Short Patches of Outliers, ARCH and Volatility Modeling

In this paper we test for (Generalized) AutoRegressive Conditional Heteroskedasticity [(G)ARCH] in daily data on 22 exchange rates and 13 stock market indices using the standard Lagrange Multiplier [LM] test for GARCH and a LM test that is resistant to patches of additive outliers. The data span two samples of 5 years ranging from 1986 to 1995. Using asymptotic arguments and Monte Carlo simulations, in which we evaluate our empirical method, we show that patches of outliers can have significant effects on test outcomes. Our main empirical result is that we find spurious GARCH in about 40% of the cases, while in many other cases we find evidence of GARCH even though such sequences of extraordinary observations seem to be present.