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A simple approach to standardized-residuals-based higher-moment tests

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  • Chen, Yi-Ting

Abstract

We propose a new approach to the higher-moment tests for evaluating the standardized error distribution hypothesis of a conditional mean-and-variance model (such as a GARCH-type model). Our key idea is to purge the effect of estimating the conditional mean-and-variance parameters on the estimated higher moments by suitably using the first and second moments of the standardized residuals. The resulting higher-moment tests have a simple invariant form for various conditional mean-and-variance models, and are also applicable to the symmetry or independence hypothesis that does not involve a complete standardized error distribution. Thus, our tests are simple and flexible. Using our approach, we establish a class of skewness–kurtosis tests, characteristic-function-based moment tests, and Value-at-Risk tests for exploring the standardized error distribution and higher-order dependence structures. We also conduct a simulation to show the validity of our approach in purging the estimation effect, and provide an empirical example to show the usefulness of our tests in exploring conditional non-normality.

Suggested Citation

  • Chen, Yi-Ting, 2012. "A simple approach to standardized-residuals-based higher-moment tests," Journal of Empirical Finance, Elsevier, vol. 19(4), pages 427-453.
  • Handle: RePEc:eee:empfin:v:19:y:2012:i:4:p:427-453
    DOI: 10.1016/j.jempfin.2012.04.006
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    Cited by:

    1. Bontemps, Christian, 2013. "Moment-Based Tests for Discrete Distributions," IDEI Working Papers 772, Institut d'Économie Industrielle (IDEI), Toulouse, revised Oct 2014.
    2. Bontemps, Christian, 2014. "Simple moment-based tests for value-at-risk models and discrete distribution," TSE Working Papers 14-535, Toulouse School of Economics (TSE).

    More about this item

    Keywords

    Conditional distribution; Estimation effect; GARCH-type models; Higher-moment tests; Standardized errors;

    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
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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