Modelling Seasonal Volatility and Level Shift in Fractionally Integrated Processes

This chapter introduces a class of seasonal fractionally integrated autoregressive moving average-generalized conditional heteroscedasticity (SARFIMAGARCH) models, with level shift type intervention that are capable of capturing simultaneously four key features of time series: seasonality, long range dependence, volatility and level shift. The main focus is on modelling seasonal level shift (SLS) in fractionally integrated and volatile processes. A natural extension of the seasonal level shift detection test of the mean for a realization of time series satisfying SLS-SARFIMA and SLS-GARCH models was derived. Test statistics that are useful to examine if seasonal level shift in an SARFIMA-GARCH model is statistically plausible were introduced. Estimation of SLS-SARFIMA and SLS-GARCH parameters are also given.