On Attempts to Use Models Incorporating Long-Range Dependence in Long-Term Volatility Forecasting

Abstract

ARFIMA models, as advocated by Jiang and Tian for use in long-term volatility forecasting, are found in a follow-up empirical study to be dominated by a certain simple historical predictor of stock price volatility at a five-year horizon. (This particular historical predictor is not recommended over more conventional methods, such as fifteen-year trailing historical volatility, due to bias-related concerns.) A relationship is observed between the estimated fractional-differencing parameter and the predictability of volatility. For companies with estimated values of d around 0.3, volatility forecast-errors (using several forecast methods) are significantly smaller than for those with estimated d in the range of about (0.4, 0.5). Negative coefficients on ARFIMA forecasts, after controlling for long-run historical volatility within certain multivariate volatility prediction-models, is suggestive of a relationship between ARFIMA prediction-results and phenomena like structural breaks, which are not captured by the ARFIMA approach.