Combining Long Memory and Level Shifts in Modeling and Forecasting the Volatility of Asset Returns

We propose a parametric state space model with accompanying estimation and forecasting framework that combines long memory and level shifts by decomposing the underlying process into a simple mixture model and ARFIMA dynamics. The Kalman filter is used to construct the likelihood function after augmenting the probability of states by a mixture of normally distributed processes. The forecasts are constructed by exploiting the information in the Kalman recursions. The validity of the estimation methodology is shown through a comprehensive simulation study. Besides being able to identify the true memory of a process, the model consistently belongs to the 10% Model Confidence Set when considering out-of-sample forecasting performance as the only one among four competing dynamic models for all forecasting horizons when applied to high frequency stock- and bond market data together with time series of daily returns on stock market and exchange rate data. As a by-product, we provide simulation and empirical evidence of the "Spurious Break" phenomenon when estimating the number of level shifts in structural models for I(d) processes.