Evaluating Volatility Forecasts with Ultra-High-Frequency Data—Evidence from the Australian Equity Market

Abstract

Due to the unobserved nature of the true return variation process, one of the most challenging problems in evaluation of volatility forecasts is to find an accurate benchmark proxy for ex - post volatility. This paper uses the Australia n equity market ultra-high-frequency data to construct an unbiased ex - post volatility estimator and then use it as a benchmark to evaluate various practical volatility forecasting strategies (GARCH class model based). These forecasting strategies allow for the skewed distribution of innovations and use various estimation windows in addition to the standard GARCH volatility models. In out-of-sample tests, we find that forecasting errors across all model specifications are systematically reduced if using the unbiased ex - post volatility estimator compared with those using the realized volatility based on sparsely sampled intra-day data. In particular, we show that the three benchmark forecasting models outperform most of the modified strategies with different distribution of returns and estimation windows. Comparing the three standard GARCH class models, we find that the asymmetric power ARCH (APARCH) model exhibits the best forecasting power in both normal and financial turmoil periods, which indicates the ability of APARCH model to capture the leptokurtic returns and stylized features of volatility in the Australian stock market.