This paper tries to select a plausibe heteroskedastic time series model which explains the daily logarithmic returns of the Nikkei 225 index of the Tokyo Stock Exchange from Jan.4, 1950 through Dec.30, 1999. Several new summary statistics are presented for this purpose. The results depend on its subperiods. On the average, among AR(1), ARMA(1,1) and nine GARCH type models we studied, ARMA(1,1)-GARCH(1,1) model is found to be plausible.