Whittle estimation of EGARCH and other exponential volatility models

Abstract

The strong consistency and asymptotic normality of the Whittle estimate of the parameters in a class of exponential volatility processes are established. Our main focus here are the EGARCH model of [Nelson, D. 1991. Conditional heteroscedasticity in asset pricing: a new approach. Econometrica 59, 347–370] and other one-shock models such as the GJR model of [Glosten, L., Jaganathan, R., Runkle, D., 1993. On the relation between the expected value and the volatility of the nominal excess returns on stocks. Journal of Finance, 48, 1779–1801], but two-shock models, such as the SV model of [Taylor, S. 1986. Modelling Financial Time Series. Wiley, Chichester (UK)], are also comprised by our assumptions. The variable of interest might not have finite fractional moment of any order and so, in particular, finite variance is not imposed. We allow for a wide range of degrees of persistence of shocks to conditional variance, allowing for both short and long memory.