A Source of Long Memory in Volatility

The long memory characteristic of financial market volatility is well documentedand has important implications for volatility forecasting and optionpricing. When fitted to the same data, different volatility models calculate theunconditional variance differently and could have very different volatility persistentparameters. Hence, they produce very different volatility forecasts evenwhen the projection is just beyond a few days. The popular GARCH and GJRmodels have short memory. This paper compares the out-of-sample forecastingperformance of four long memory volatility models, viz. fractional integrated(FI), break, component and regime switching. Using S&P 500 returns, we findstructural break model to produce the best in-sample fit and out-of-sampleforecasts, if future volatility breaks are known. Without knowing the futurebreaks, GJR produced the best short horizon forecasts. For volatility forecastsof 10 days and beyond, FI dominates....