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Size Distortion in the Analysis of Volatility and Covolatility Effects

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Uncertainty Analysis in Econometrics with Applications

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 200))

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Abstract

Let us assume that \(\hat{A}_T\) is a consistent, asymptotically normal estimator of a matrix A (where T is the sample size), this paper shows that test statistics used in empirical work to test 1) the noninvertibility of A, i.e. det A = 0, 2) the positivite semi-definiteness A > > 0, have a different asymptotic distribution in the case where A = 0 than in the case where A ≠ 0. Moreover, the paper shows that an estimator of A constrained by symmetry or reduced rank has a different asymptotic distribution when A = 0 than when A ≠ 0. The implication is that inference procedures that use critical values equal to appropriate quantiles from the distribution when A ≠ 0 may be size distorted. The paper points out how the above statistical problems arise in standard models in Finance in the analysis of risk effects.A Monte Carlo study explores how the asymptotic results are reflected in finite sample.

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Author information

Authors and Affiliations

  1. CREST, CEPREMAP and University of Toronto, Toronto, France

    Christian Gourieroux

  2. York University, York, Canada

    Joann Jasiak

Authors
  1. Christian Gourieroux
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  2. Joann Jasiak
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Correspondence to Christian Gourieroux .

Editor information

Editors and Affiliations

  1. Science and Technology, School of Knowledge Science, Japan Advanced Institute of, Asahidai, Nomi 1-1, Ishikawa, 923-1292, Japan

    Van-Nam Huynh

  2. , Department of Computer Science, University of Texas at El Paso, W. University 500, El Paso, 79968, Texas, USA

    Vladik Kreinovich

  3. , Faculty of Economics, Chiang Mai University, Chinag Mai, 50200, Thailand

    Songsak Sriboonchitta

  4. , Faculty of Economics, Chiang Mai University, Chinag Mai, 50200, Thailand

    Komsan Suriya

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Gourieroux, C., Jasiak, J. (2013). Size Distortion in the Analysis of Volatility and Covolatility Effects. In: Huynh, VN., Kreinovich, V., Sriboonchitta, S., Suriya, K. (eds) Uncertainty Analysis in Econometrics with Applications. Advances in Intelligent Systems and Computing, vol 200. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35443-4_7

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  • DOI: https://doi.org/10.1007/978-3-642-35443-4_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-35442-7

  • Online ISBN: 978-3-642-35443-4

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