The Bias in Time-Series Volatility Forecasts

By Jensen's inequality, a model's forecasts of the variance and standard deviation of returns cannot both be unbiased. This paper explores the bias in GARCH type model forecasts of the standard deviation of returns, which we argue is the more appropriate volatility measure for most financial applications. For a wide variety of markets, the GARCH, EGARCH, and GJR (or TGARCH) models tend to persistently over-estimate the standard deviation of returns while the ARLS model of Ederington and Guan (2005, JFM) does not. Furthermore, the GARCH and GJR forecasts are especially biased following high volatility days which cause a large jump in forecast volatility which is rarely fully realized