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Modelling and forecasting long memory time series with Exponential and Switching GARCH models

There is some evidence that structural change or stochastic regime switching and long memory are intimately related concepts. However, long memory and regime switching in a stochastic process are properties that could be easily confused in a financial study. Using a modelling approach, the aim is to distinguish regime switching behaviour from long memory for the financial time series. In an empirical study the forecasting performance of symmetric, asymmetric, long memory and Markov switching GARCH model are compared using Tehran stock market daily returns. The results indicate that in out of sample performance, long memory exponential GARCH (FIEGARCH) model outperforms the competing models. To ensure the validity of the results, the value at risk (VaR) forecasts are obtained for each model and a loss function is calculated. A simple rule for distinguishing between long memory and structural break in financial and economic time series is suggested.