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

Author

Listed:
  • 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.

Suggested Citation

  • Jushan Bai & Serena Ng, 2001. "Tests for Skewness, Kurtosis, and Normality for Time Series Data," Boston College Working Papers in Economics 501, Boston College Department of Economics.
  • Handle: RePEc:boc:bocoec:501
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    References listed on IDEAS

    as
    1. Andrews, Donald W K & Monahan, J Christopher, 1992. "An Improved Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimator," Econometrica, Econometric Society, vol. 60(4), pages 953-966, July.
    2. J. Bradford De Long & Lawrence H. Summers, 1984. "Are Business Cycles Symmetric?," NBER Working Papers 1444, National Bureau of Economic Research, Inc.
    3. Caballero, Ricardo J, 1992. "A Fallacy of Composition," American Economic Review, American Economic Association, vol. 82(5), pages 1279-1292, December.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    symmetry; kurtosis; normality; Bera-Jarque test;

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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