Tests for Skewness, Kurtosis, and Normality for Time Series Data
给出了时间序列数据中偏度系数、峰度系数以及联合正态性检验的抽样分布，并说明在序列相关时需要估计长期协方差矩阵。蒙特卡洛模拟显示对称性和正态性检验有良好的有限样本性质，但峰度检验仅对薄尾分布有效。
AbstractWe present the sampling distributions for the coefficient of skewness, kurtosis, and a joint test of normality for time series observations. We show that when the data are serially correlated, consistent estimates of three-dimensional long-run covariance matrices are needed for testing symmetry or kurtosis. These tests can be used to make inference about any conjectured coefficients of skewness and kurtosis. In the special case of normality, a joint test for the skewness coefficient of 0 and a kurtosis coefficient of 3 can be obtained on construction of a four-dimensional long-run covariance matrix. The tests are developed for demeaned data, but the statistics have the same limiting distributions when applied to regression residuals. Monte Carlo simulations show that the test statistics for symmetry and normality have good finite-sample size and power. However, size distortions render testing for kurtosis almost meaningless except for distributions with thin tails, such as the normal distribution. Combining skewness and kurtosis is still a useful test of normality provided that the limiting variance accounts for the serial correlation in the data. The tests are applied to 21 macroeconomic time series.KEY WORDS: Jarque–Bera testKurtosisNormalitySymmetry