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The Likelihood Function of Conditionally Heteroskedastic Factor Models

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  • Enrique Sentana

Abstract

We derive the likelihood function and score of factor models with dynamic heteroskedasticity, and the Kuhn-Tucker conditions defining the inequality restricted maximum likelihood estimators that guarantee a positive definite convariance matrix. We present three methods to compute the likelihood function, its gradient and factor scores, which are numerically efficient and reliable, and statistically sound. We show that the incidence of zero idiosyncratic variance estimates (Heywood cases) depends on the correlation of a variable with the rest.

Suggested Citation

  • Enrique Sentana, 2000. "The Likelihood Function of Conditionally Heteroskedastic Factor Models," Annals of Economics and Statistics, GENES, issue 58, pages 1-19.
    • Handle: RePEc:adr:anecst:y:2000:i:58:p:1-19
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    File URL: http://www.jstor.org/stable/20076226
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    Cited by:

    1. Sentana, Enrique & Fiorentini, Gabriele, 2001. "Identification, estimation and testing of conditionally heteroskedastic factor models," Journal of Econometrics, Elsevier, vol. 102(2), pages 143-164, June.
    2. Sentana, Enrique, 2004. "Factor representing portfolios in large asset markets," Journal of Econometrics, Elsevier, vol. 119(2), pages 257-289, April.
    3. M. Hashem Pesaran & Bahram Pesaran, 2007. "Volatilities and Conditional Correlations in Futures Markets with a Multivariate t Distribution," CESifo Working Paper Series 2056, CESifo.
    4. Gabriele Fiorentini & Enrique Sentana, 2009. "Dynamic Specification Tests for Static Factor Models," Working Papers wp2009_0912, CEMFI.
    5. Pesaran, Bahram & Pesaran, M. Hashem, 2007. "Modelling Volatilities and Conditional Correlations in Futures Markets with a Multivariate t Distribution," IZA Discussion Papers 2906, Institute of Labor Economics (IZA).
    6. Gregory Bauer & Antonio Diez de los Rios, 2012. "An International Dynamic Term Structure Model with Economic Restrictions and Unspanned Risks," Staff Working Papers 12-5, Bank of Canada.
    7. Fiorentini, Gabriele & Galesi, Alessandro & Sentana, Enrique, 2018. "A spectral EM algorithm for dynamic factor models," Journal of Econometrics, Elsevier, vol. 205(1), pages 249-279.
    8. Pesaran, Bahram & Pesaran, M. Hashem, 2010. "Conditional volatility and correlations of weekly returns and the VaR analysis of 2008 stock market crash," Economic Modelling, Elsevier, vol. 27(6), pages 1398-1416, November.
    9. Enrique Sentana & Giorgio Calzolari & Gabriele Fiorentini, 2004. "Indirect Estimation of Conditionally Heteroskedastic Factor Models," Working Papers wp2004_0409, CEMFI.
    10. Gabriele Fiorentini & Enrique Sentana, 2007. "On the efficiency and consistency of likelihood estimation in multivariate conditionally heteroskedastic dynamic regression models," Working Paper series 38_07, Rimini Centre for Economic Analysis.

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