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

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  • Jushan Bai
  • Serena Ng

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.

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Article provided by American Statistical Association in its journal Journal of Business and Economic Statistics.

Volume (Year): 23 (2005)
Issue (Month): (January)
Pages: 49-60

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Handle: RePEc:bes:jnlbes:v:23:y:2005:p:49-60

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  1. J. Bradford De Long & Lawrence H. Summers, 1986. "Are Business Cycles Symmetric?," NBER Working Papers 1444, National Bureau of Economic Research, Inc.
  2. Donald W.K. Andrews & Christopher J. Monahan, 1990. "An Improved Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimator," Cowles Foundation Discussion Papers 942, Cowles Foundation for Research in Economics, Yale University.
  3. Caballero, R.J., 1990. "A Fallacy Of Composition," Discussion Papers 1990_01, Columbia University, Department of Economics.
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