Semiparametric ARCH-X Model for Leverage Effect and Long Memory in Stock Return Volatility

This paper investigates a new semiparametric ARCH-X model to account for both leverage effect and long memory property in volatility. It is a partial linear model combining a nonparametric ARCH component and an exogenous covariate that is persistent in memory. This model can allow for a flexible functional form of the asymmetric relationship between stock return and volatility and generate the long memory property in volatility. We adopt a realized volatility measure as the covariate in our model. For the daily FTSE 100 Index return series, the nonparametric component of our model captures the leverage effect and is estimated to be a complex nonlinear function. It is shown that our model outperforms other parametric or nonparametric volatility models both in within-sample and out-of-sample forecasts.