Recursive modelling of symmetric and asymmetric volatility in the presence of extreme observations

This paper is concerned with recursive estimation, testing and forecasting of the asymmetric volatility of daily returns in Standard and Poor's 500 Composite Index and the Nikkei 225 Index in the presence of extreme observations, or significant spikes in the volatility of daily returns. For each of the two data sets, the empirical analysis increases the sample size up to 12000 observations recursively to examine the effects of extreme observations on: (i) the Quasi Maximum Likelihood Estimates (QMLE) of the GARCH(1,1) and asymmetric GJR(1,1) parameters; (ii) the associated asymptotic and robust t-ratios of the QMLE; (iii) recursive statistical testing of the asymmetry parameter in GJR(1,1); (iv) the sufficient second and fourth moment conditions for consistency and asymptotic normality, respectively, of the QMLE of GARCH(1,1) and GJR(1,1); and (v) the forecast performance of the GARCH(1,1) and GJR(1,1) models for periods with significant spikes in volatility and for periods of relative calm.