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Likelihood-based estimation of latent generalised ARCH

Author

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  • Neil Shephard
  • Enrique Sentana
  • Gabriele Fiorentini

Abstract

GARCH models are commonly used as latent processes in econometrics, financial economics and macroeconomics. Yet no exact likelihood analysis of these models has been provided so far. In this paper we outline the issues and suggest a Markov chain Monte Carlo algorithm which allows the calculation of a classical estimator via the simulated EM algorithm or a Bayesian solution in O(T) computational operations, where T denotes the sample size. We assess the performance of our proposed algorithm in the context of both artificial examples and an empirical application to 26 UK sectorial stock returns, and compare it to existing approximate solutions. GARCH models are commonly used as latent processes in econometrics, financial economics and macroeconomics.

Suggested Citation

  • Neil Shephard & Enrique Sentana & Gabriele Fiorentini, 2003. "Likelihood-based estimation of latent generalised ARCH," Economics Series Working Papers 2004-FE-02, University of Oxford, Department of Economics.
    • Handle: RePEc:oxf:wpaper:2004-fe-02
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    Cited by:

    1. Poncela, Pilar & Ruiz, Esther & Miranda, Karen, 2021. "Factor extraction using Kalman filter and smoothing: This is not just another survey," International Journal of Forecasting, Elsevier, vol. 37(4), pages 1399-1425.
    2. Catherine Doz & Eric Renault, 2004. "Conditionally Heteroskedastic Factor Models: Identification and Instrumental Variables Estimation," CIRANO Working Papers 2004s-37, CIRANO.
    3. Broto, Carmen, 2006. "Using auxiliary residuals to detect conditional heteroscedasticity in inflation," DES - Working Papers. Statistics and Econometrics. WS ws060402, Universidad Carlos III de Madrid. Departamento de Estadística.

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