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A Test for Conditional Symmetry in Time Series Models

Author

Listed:
  • Jushan Bai

    () (Boston College)

  • Serena Ng

    () (Boston College)

Abstract

The assumption of conditional symmetry is often invoked to validate adaptive estimation and consistent estimation of ARCH/GARCH models by quasi maximum likelihood. Imposing conditional symmetry can increase the efficiency of bootstraps if the symmetry assumption is valid. This paper proposes a procedure for testing conditional symmetry. The proposed test does not require the data to be stationary or i.i.d., and the dimension of the conditional variables could be infinite. The size and power of the test are satisfactory even for small samples. In addition, the proposed test is shown to have non-trivial power against root-T local alternatives. Applying the test to various time series, we reject conditional symmetry in inflation, exchange rate and stock returns. These data have previously been tested and rejected for unconditional symmetry. Among the non-financial time series considered, we find that investment, the consumption of durables, and manufacturing employment also reject conditional symmetry. Interestingly, these are series whose dynamics are believed to be affected by fixed costs of adjustments.

Suggested Citation

  • Jushan Bai & Serena Ng, 1998. "A Test for Conditional Symmetry in Time Series Models," Boston College Working Papers in Economics 410, Boston College Department of Economics.
  • Handle: RePEc:boc:bocoec:410
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    File URL: http://fmwww.bc.edu/EC-P/wp410.pdf
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    References listed on IDEAS

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    3. Whitney K. Newey & Douglas G. Steigerwald, 1997. "Asymptotic Bias for Quasi-Maximum-Likelihood Estimators in Conditional Heteroskedasticity Models," Econometrica, Econometric Society, vol. 65(3), pages 587-600, May.
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    5. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
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    7. Lee, Sang-Won & Hansen, Bruce E., 1994. "Asymptotic Theory for the Garch(1,1) Quasi-Maximum Likelihood Estimator," Econometric Theory, Cambridge University Press, vol. 10(01), pages 29-52, March.
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    Cited by:

    1. Ruge-Murcia, Francisco J, 2003. " Inflation Targeting under Asymmetric Preferences," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 35(5), pages 763-785, October.

    More about this item

    Keywords

    conditional symmetry; empirical distribution function; kernel estimation; Brownian motion; ARCH/GARCH; nonlinear timeseries;

    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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