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A Test for Conditional Symmetry in Time Series Models

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  • 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.

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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 410.

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Length: 34 pages
Date of creation: 27 Aug 1998
Date of revision:
Handle: RePEc:boc:bocoec:410

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

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  1. Stoker, Thomas M, 1986. "Consistent Estimation of Scaled Coefficients," Econometrica, Econometric Society, Econometric Society, vol. 54(6), pages 1461-81, November.
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  4. Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
  5. Whitney K. Newey & Douglas G. Steigerwald, 1997. "Asymptotic Bias for Quasi-Maximum-Likelihood Estimators in Conditional Heteroskedasticity Models," Econometrica, Econometric Society, Econometric Society, vol. 65(3), pages 587-600, May.
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  11. Beaudry, Paul & Koop, Gary, 1993. "Do recessions permanently change output?," Journal of Monetary Economics, Elsevier, Elsevier, vol. 31(2), pages 149-163, April.
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Cited by:
  1. Ruge-Murcia, F.J., 2001. "Inflation Targeting Under Asymmetric Preferences," Cahiers de recherche, Centre interuniversitaire de recherche en économie quantitative, CIREQ 2001-04, Centre interuniversitaire de recherche en économie quantitative, CIREQ.

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