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

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  • Jushan Bai

    ()
    (Boston College)

  • Serena Ng

    ()
    (Boston College)

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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Bibliographic Info

Paper provided by Boston College Department of Economics in its series Boston College Working Papers in Economics with number 501.

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Length: 18 pages
Date of creation: 15 Jun 2001
Date of revision:
Handle: RePEc:boc:bocoec:501

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Keywords: symmetry; kurtosis; normality; Bera-Jarque test;

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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. Ricardo J. Caballero, 1991. "A Fallacy of Composition," NBER Working Papers 3735, National Bureau of Economic Research, Inc.
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