Garch-Type Models and Performance of Information Criteria

Abstract

GARCH model has gained popularity during the last two decades, because of their ability to capture non-linear dynamics in the real life data which we often observe especially in financial markets. This paper discuss four common information criteria (AIC, AICc, BIC and HQ) and their ability of correct selection in the presence of GARCH effect, based on their probability of correct selection as a measure of performance. The investigation has been performed using Monte Carlo simulation of conditional variance GARCH processes with six different kinds of DGPs including; GARCH(p, q), p = 1, 2 and q = 1, 2, GARCH(1, 1)-Leverage, and GARCH(1, 1)-Spillover. All these models are further simulated with different parameter combinations to study the possible effect of different volatility structures on these information criteria. We notice an impact from the volatility structure of time series on the performance of these criteria. Specially for higher order GARCH processes, the BIC and HQ criterion select the lower order process at small sample size. Furthermore, we observe different behavior of information criteria for changing the parameter set in higher order case. Moreover, the influence of sample size, having an impact on the the performance of these criteria towards correct selection, is observed.