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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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    3. Anderson, G. J., 1980. "The structure of simultaneous equations estimators : A comment," Journal of Econometrics, Elsevier, vol. 14(2), pages 271-276, October.
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    5. 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.).
    6. Engle, Robert F. & Granger, C. W. J. & Kraft, Dennis, 1984. "Combining competing forecasts of inflation using a bivariate arch model," Journal of Economic Dynamics and Control, Elsevier, vol. 8(2), pages 151-165, November.
    7. Engle, Robert F & Lilien, David M & Robins, Russell P, 1987. "Estimating Time Varying Risk Premia in the Term Structure: The Arch-M Model," Econometrica, Econometric Society, vol. 55(2), pages 391-407, March.
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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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