Type 1 error rate and significance levels when using GARCH-type models

Abstract: The purpose of this thesis is to test whether the probability of falsely rejecting a true null hypothesis of a model intercept being equal to zero is consistent with the chosen significance level when modelling the variance of the error term using GARCH (1,1), TGARCH (1,1) or IGARCH (1,1) models. We test this by estimating “Jensen’s alpha” to evaluate alpha trading, using a Monte Carlo simulation based on historical data from the Standard & Poor’s 500 Index and stocks in the Dow Jones Industrial Average Index. We evaluate over simulated daily data ranging over periods of 3 months, 6 months, and 1 year. Our results indicate that the GARCH and IGARCH consistently reject a true null hypothesis less often than the selected 1%, 5%, or 10%, whereas the TGARCH consistently rejects a true null more often than the chosen significance level. Thus, there is a risk of incorrect inferences when using these GARCH-type models.