A comparison of seasonal volatility models

Abstract

Financial market data exhibits various forms of seasonal behaviour. In this work, the problem of seasonal effects on volatility models is discussed. We introduce moving average and autoregressive moving average representation with multiplicative seasonal GARCH errors. Derived an expression for the variance of the m-steps ahead forecast error of MA(q) model with seasonal GARCH errors and also for the squared series Yn+m. We also derived the expressions for the kurtosis of the error distribution. The evidence-based approach is carried out in R software. Real data set is used to illustrate the theoretical results.