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Asymptotic Theory for ARCH Models: Estimation and Testing

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  • Weiss, Andrew A.

Abstract

In the context of a linear dynamic model with moving average errors, we consider a heteroscedastic model which represents an extension of the ARCH model introduced by Engle [4]. We discuss the properties of maximum likelihood and least squares estimates of the parameters of both the regression and ARCH equations, and also the properties of various tests of the model that are available. We do not assume that the errors are normally distributed.

Suggested Citation

  • Weiss, Andrew A., 1986. "Asymptotic Theory for ARCH Models: Estimation and Testing," Econometric Theory, Cambridge University Press, vol. 2(1), pages 107-131, April.
    • Handle: RePEc:cup:etheor:v:2:y:1986:i:01:p:107-131_01
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    1. Gourieroux, Christian & Holly, Alberto & Monfort, Alain, 1982. "Likelihood Ratio Test, Wald Test, and Kuhn-Tucker Test in Linear Models with Inequality Constraints on the Regression Parameters," Econometrica, Econometric Society, vol. 50(1), pages 63-80, January.
    2. Z. Lomnicki, 1961. "Tests for departure from normality in the case of linear stochastic processes," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 4(1), pages 37-62, December.
    3. Dhrymes, Phoebus J & Taylor, John B, 1976. "On an Efficient Two-Step Estimator for Dynamic Simultaneous Equations Models with Autoregressive Errors," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 17(2), pages 362-376, June.
    4. A. R. Pagan & A. D. Hall & P. K. Trivedi, 1983. "Assessing the Variability of Inflation," Review of Economic Studies, Oxford University Press, vol. 50(4), pages 585-596.
    5. White, Halbert & Domowitz, Ian, 1984. "Nonlinear Regression with Dependent Observations," Econometrica, Econometric Society, vol. 52(1), pages 143-161, January.
    6. Godfrey, Leslie G, 1978. "Testing against General Autoregressive and Moving Average Error Models When the Regressors Include Lagged Dependent Variables," Econometrica, Econometric Society, vol. 46(6), pages 1293-1301, November.
    7. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
    8. 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.
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