Tests for Skewness, Kurtosis, and Normality for Time Series Data

Jushan Bai () and Serena Ng ()

No 501, Boston College Working Papers in Economics from Boston College Department of Economics

Abstract: We present the sampling distributions for the coefficient of skewness, kurtosis, and a joint test of normality for time series observations. In contrast to independent and identically distributed data, the limiting distributions of the statistics are shown to depend on the long run rather than the short-run variance of relevant sample moments. 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. Nevertheless, this general weakness of testing for kurtosis is of little consequence for testing normality. Combining skewness and kurtosis as in Bera and Jarque (1981) is still a useful test of normality provided the limiting variance accounts for the serial correlation in the data.

Keywords: symmetry; kurtosis; normality; Bera-Jarque test (search for similar items in EconPapers)
JEL-codes: C12 C22 (search for similar items in EconPapers)
Date: 2001-06-15
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Journal Article: Tests for Skewness, Kurtosis, and Normality for Time Series Data (2005)
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