Asymptotic Theory for ARCH Models: Estimation and Testing

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.

[1]  Bronwyn H Hall,et al.  Estimation and Inference in Nonlinear Structural Models , 1974 .

[2]  B. G. Quinn,et al.  Random Coefficient Autoregressive Models: An Introduction , 1982 .

[3]  R. Engle Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation , 1982 .

[4]  L. Godfrey TESTING AGAINST GENERAL AUTOREGRESSIVE AND MOVING AVERAGE ERROR MODELS WHEN THE REGRESSORS INCLUDE LAGGED DEPENDENT VARIABLES , 1978 .

[5]  A. Milhøj The moment structure of ARCH processes , 1985 .

[6]  H. White,et al.  Nonlinear Regression with Dependent Observations , 1984 .

[7]  H. White Maximum Likelihood Estimation of Misspecified Models , 1982 .

[8]  Phoebus J. Dhrymes,et al.  On an Efficient Two-Step Estimator for Dynamic Simultaneous Equations Models with Autoregressive Errors , 1976 .

[9]  Jorma Rissanen,et al.  THE STRONG CONSISTENCY OF MAXIMUM LIKELIHOOD ESTIMATORS FOR ARMA PROCESSES , 1979 .

[10]  Adrian Pagan,et al.  Assessing the variability of inflation , 1983 .

[11]  C. Gouriéroux,et al.  Likelihood Ratio Test, Wald Test, and Kuhn-Tucker Test in Linear Models with Inequality Constraints on the Regression Parameters , 1982 .

[12]  C. Granger Advances in Econometrics: Generating mechanisms, models, and causality , 1983 .

[13]  Z. A. Lomnicki Tests for departure from normality in the case of linear stochastic processes , 1961 .

[14]  Barry G. Quinn,et al.  Random Coefficient Autoregressive Models: An Introduction. , 1984 .

[15]  A. A. Weiss ARMA MODELS WITH ARCH ERRORS , 1984 .