An integrated heteroscedastic autoregressive model for forecasting realized volatilities

A new strategy for forecasting realized volatility (RV) is proposed for the heteroscedastic autoregressive (HAR) model of Corsi (2009). The strategy is constraining the sum of the HAR coefficients to one, resulting in an integrated model, called IHAR model. The IHAR model is motivated by stationarity of estimated HAR model, downward biases of estimated HAR coefficients, and over-rejection of ADF test for long-memory processes. Considerable out-of-sample forecast improvements of the IHAR model over the HAR model are demonstrated for RVs of 4 financial assets: the US S&P 500 index, the US NASDAQ index, the Japan yen/US dollar exchange rate, and the EU euro/US dollar exchange rate. Forecast improvement is also verified in a Monte Carlo experiment and in an empirical comparison for an extended data set. The forecast improvement is shown to be a consequence of the fact that the IHAR model takes better advantage of the long memory of RV and the conditional heteroscedasticity of RV than the HAR model.