Excess kurtosis of conditional distribution for daily stock returns: the case of Japan

Abstract

Not only the unconditional distribution but also the conditional distribution of daily asset returns are known to be leptokurtic. Thus, some authors have suggested using ARCH-type models with leptokurtic distributions such as the t-distribution and the generalized error distribution (GED) for the conditional distribution. The purpose of this paper examines what distribution is fit for the conditional distribution of daily Japanese stock returns. In particular, we estimate an exponential GARCH (EGARCH) model developed by Nelson (1991) jointly with the generalized t-distribution, which nests both the Student's t-distribution and the generalized error distribution (GED) employed by other researchers. It is shown that the Student's t-distribution is suited for capturing the excess kurtosis of conditional distribution for daily Japanese stock returns, which does not depend on sample period and is consistent with what Bollerslev et al. (1994) have found by fitting a similar model to daily US stock returns.