Testing for EGARCH Against Stochastic Volatility Models

It is shown that the EGARCH model is the degenerate case of Danielsson's [Journal of Econometrics (1994) Vol. 61, pp. 375-400] stochastic volatility model where the disturbance of the transition equation of conditional volatility has zero variance. The Lagrange multiplier test statistic is obtained for the EGARCH model against the stochastic volatility model by expressing the degenerate density under the null hypothesis by the Dirac delta function. The finite sample performance of the test is studied in a small Monte Carlo experiment. Copyright 2005 Blackwell Publishing Ltd.