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Multivariate Simultaneous Generalized ARCH

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Author Info
Engle, Robert F.
Kroner, Kenneth F.

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Abstract

This paper presents theoretical results on the formulation and estimation of multivariate generalized ARCH models within simultaneous equations systems. A new parameterization of the multivariate ARCH process is proposed, and equivalence relations are discussed for the various ARCH parameterizations. Constraints sufficient to guarantee the positive definiteness of the conditional covariance matrices are developed, and necessary and sufficient conditions for covariance stationarity are presented. Identification and maximum likelihood estimation of the parameters in the simultaneous equations context are also covered.

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Publisher Info
Article provided by Cambridge University Press in its journal Econometric Theory.

Volume (Year): 11 (1995)
Issue (Month): 01 (February)
Pages: 122-150
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Handle: RePEc:cup:etheor:v:11:y:1995:i:01:p:122-150_00

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. McCurdy, Thomas H & Morgan, Ieuan G, 1991. "Tests for a Systematic Risk Component in Deviations from Uncovered Interest Rate Parity," Review of Economic Studies, Blackwell Publishing, vol. 58(3), pages 587-602, May. [Downloadable!] (restricted)
  2. McCurdy, Thomas H & Morgan, Ieuan G, 1988. "Testing the Martingale Hypothesis in Deutsche Mark Futures with Models Specifying the Form of Heteroscedasticity," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 3(3), pages 187-202, July-Sept. [Downloadable!] (restricted)
  3. Kroner, Kenneth F. & Claessens, Stijn, 1991. "Optimal dynamic hedging portfolios and the currency composition of external debt," Journal of International Money and Finance, Elsevier, vol. 10(1), pages 131-148, March. [Downloadable!] (restricted)
  4. Friedman, Milton, 1977. "Nobel Lecture: Inflation and Unemployment," Journal of Political Economy, University of Chicago Press, vol. 85(3), pages 451-72, June. [Downloadable!] (restricted)
  5. 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. [Downloadable!] (restricted)
  6. Bollerslev, Tim & Chou, Ray Y. & Kroner, Kenneth F., 1992. "ARCH modeling in finance : A review of the theory and empirical evidence," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 5-59. [Downloadable!] (restricted)
  7. E.K. Berndt & B.H. Hall & R.E. Hall, 1974. "Estimation and Inference in Nonlinear Structural Models," NBER Chapters, in: Annals of Economic and Social Measurement, Volume 3, number 4, pages 103-116 National Bureau of Economic Research, Inc. [Downloadable!]
  8. Tim Bollerslev & Jeffrey Wooldridge, 1992. "Quasi-maximum likelihood estimation and inference in dynamic models with time-varying covariances," Econometric Reviews, Taylor and Francis Journals, vol. 11(2), pages 143-172. [Downloadable!] (restricted)
  9. Kaminsky, Graciela & Peruga, Rodrigo, 1990. "Can a time-varying risk premium explain excess returns in the forward market for foreign exchange?," Journal of International Economics, Elsevier, vol. 28(1-2), pages 47-70, February. [Downloadable!] (restricted)
  10. Lee, Sang-Won & Hansen, Bruce E., 1994. "Asymptotic Theory for the Garch(1,1) Quasi-Maximum Likelihood Estimator," Econometric Theory, Cambridge University Press, vol. 10(01), pages 29-52, March. [Downloadable!]
  11. Tim Bollerslev & Robert F. Engle & Daniel B. Nelson, 1993. "ARCH Models," University of California at San Diego, Economics Working Paper Series 93-49, Department of Economics, UC San Diego. [Downloadable!]
    Other versions:
    • Bollerslev, Tim & Engle, Robert F. & Nelson, Daniel B., 1986. "Arch models," Handbook of Econometrics, in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 49, pages 2959-3038 Elsevier. [Downloadable!] (restricted)
  12. Tim Bollerslev & Jeffrey M. Wooldridge, 1988. "Quasi-Maximum Likelihood Estimation of Dynamic Models with Time-Varying Covariances," Working papers 505, Massachusetts Institute of Technology (MIT), Department of Economics.
  13. Charles Engel & Anthony P. Rodrigues, 1987. "Tests of International CAPM with Time-Varying Covariances," NBER Working Papers 2303, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
    Other versions:
  14. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April. [Downloadable!] (restricted)
  15. Kroner, Kenneth F. & Lastrapes, William D., 1993. "The impact of exchange rate volatility on international trade: Reduced form estimates using the GARCH-in-mean model," Journal of International Money and Finance, Elsevier, vol. 12(3), pages 298-318, June. [Downloadable!] (restricted)
  16. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July. [Downloadable!] (restricted)
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