Testing Gaussianity and linearity of Japanese stock returns

In this article, we first investigate the Gaussianity of Japanese stock return time series (214 daily, 18 weekly) by the Gaussianity test proposed by Kariya, Tsay, Terui and Li (1994) comprehensively and consistently. And it is observed that all the series are not Gaussian when the 6th order moment structures are taken into account. Up to the 4th order moments there are some series which are compatible with the Gaussianity. Secondly, we apply five well-known nonlinearity tests for stationary time series to the data set and examine the specific nonlinearity of the series. Some series strongly exhibit the specific types of nonlinearity. Typically the Nikkei daily index shows the TAR (Threshold Autoregressive) type nonlinearity. Comparing daily return series with weekly series, it is also shown that a central limit effect is working on the weekly stock returns, where daily information is accumulated over a week, in the sense that weekly returns are relatively closer to Gaussian.