On Measuring Volatility and the GARCH Forecasting Performance

We apply a new algorithm based on Fourier analysis to compute the volatility of a diffusion process. By using simulations of the continuous-time GARCH model, we show that our method performs well in computing integrated volatility. We show that linear interpolation of high frequency observations induces a downward bias in estimating integrated volatility. By measuring ex post volatility with our method, we find that the forecasting performance of the GARCH model is improved with respect to what is established when classical methods are employed. These results are confirmed by the analysis of exchange rate high frequency time series.