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The simultaneous equations model with generalized autoregressive conditional heteroskedasticity: the SEM-GRACH model

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  • Richard Harmon

Abstract

In this paper I generalize the standard simultaneous equations model by allowing the innovations of the structural equations to exhibit Generalized Autoregressive Conditional Heteroskedasticity (GARCH). I refer to this new specification as the SEM-GARCH model. I develop two estimation strategies: LIM-GARCH, a limited information estimator, and FIM-GARCH, a full information estimator. I show that these estimators are consistent and asymptotically normal. Following Weiss (1986) I show that when the errors in the SEM-GARCH process are incorrectly assumed to be conditionally normal the likelihood function is still maximized at the true parameters, given certain regularity conditions. This results in the asymptotic variance-covariance matrix being more complex than the usual inverse of the information matrix.

Suggested Citation

  • Richard Harmon, 1988. "The simultaneous equations model with generalized autoregressive conditional heteroskedasticity: the SEM-GRACH model," International Finance Discussion Papers 322, Board of Governors of the Federal Reserve System (U.S.).
    • Handle: RePEc:fip:fedgif:322
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    References listed on IDEAS

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    1. Domowitz, Ian & Hakkio, Craig S., 1985. "Conditional variance and the risk premium in the foreign exchange market," Journal of International Economics, Elsevier, vol. 19(1-2), pages 47-66, August.
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    6. Francis X. Diebold, 1986. "Temporal aggregation of ARCH processes and the distribution of asset returns," Special Studies Papers 200, Board of Governors of the Federal Reserve System (U.S.).
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    Cited by:

    1. Krishnakumar, Jaya & Kabili, Andi & Roko, Ilir, 2012. "Estimation of SEM with GARCH errors," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3153-3181.
    2. Emma M. Iglesias & Garry D.A. Phillips, 2004. "Multivariate Arch Models: Finite Sample Properties Of Ml Estimators And An Application To An Lm-Type Test," Working Papers. Serie AD 2004-09, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
    3. Calzolari, Giorgio & Fiorentini, Gabriele, 1994. "Conditional heteroskedasticity in nonlinear simultaneous equations," MPRA Paper 24428, University Library of Munich, Germany.

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