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This study evaluates the performance of four models for predicting daily realized volatility of S&P 500 index (SPX), Dow Jones Industry Average (DJIA), Canadian dollar (CAD/USD) and British Pound (USD/GBP) exchange rates. The competing models include a Simple Regression Model (SRM), Stochastic Volatility model with Lagged inter-temporal dependence (SVL), Stochastic Volatility model with Contemporaneous dependence (SVC), and a Heterogeneous Autoregressive (HAR) model. The main purpose is to examine whether allowing asymmetric relationships between return and volatility and leptokurtosis, or modelling the long-memory behaviour of volatility, would result in an improvement in forecast accuracy. Different approaches are considered when constructing daily realized volatility. Employing realized volatility in the in-sample estimation, the procedure is straightforward. The famous Diebold and Mariano's (1995) robust tests are applied to investigate whether the competing models provide equally accurate forecasts. Four different measures are used to evaluate the forecasting accuracy. The results suggest that allowing asymmetric behaviour and leptokurtosis do not seem to improve point forecasts, whereas modelling long-memory behaviour seems to.
