Nonparametric inferences for kurtosis and conditional kurtosis

Under the assumption of strictly stationary process,this paper proposes a nonparametric model to test the kurtosis and conditional kurtosis for risk time series.We apply this method to the daily returns of S&P500 index and the Shanghai Composite Index,and simulate GARCH data for verifying the effciency of the presented model.Our results indicate that the risk series distribution is heavily tailed,but the historical information can make its future distribution light-tailed.However the far future distribution’s tails are little affected by the historical data.