Size Distortion in the Analysis of Volatility and Covolatility Effects

  • Christian Gourieroux
  • Joann Jasiak
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 200)


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.


Multivariate Volatility Risk Premium BEKK Model Volatility Transmission Identifiability Boundary Invertibility Test 

JEL number

C10 C32 G10 G12 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.CREST, CEPREMAP and University of TorontoTorontoFrance
  2. 2.York UniversityYorkCanada

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