Articlebronze2001

WHITTLE ESTIMATION OF ARCH MODELS

90 citations0/0 files storedEconometric Theory

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Financial Risk and Volatility Modeling Stochastic processes and financial applications Complex Systems and Time Series Analysis

Abstract

For a class of parametric ARCH models, Whittle estimation based on squared observations is shown to be [square root of n]-consistent and asymptotically normal. Our conditions require the squares to have short memory autocorrelation, by comparison with the work of Zaffaroni (1999, “Gaussian Inference on Certain Long-Range Dependent Volatility Models,” Preprint), who established the same properties on the basis of an alternative class of models with martingale difference levels and long memory autocorrelated squares.

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References

1986Generalized autoregressive conditional heteroskedasticity 1992ARCH modeling in finance 1993A long memory property of stock market returns and a new model 1992Quasi-maximum likelihood estimation and inference in dynamic models with time-varying covariances 1995Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation 1990Stationarity and Persistence in the GARCH(1,1) Model 1990ARCH models as diffusion approximations 1994Asymptotic Theory for the Garch(1,1) Quasi-Maximum Likelihood Estimator

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2001Testing for long memory in the presence of a general trend 2006Pseudo-maximum likelihood estimation of ARCH$(\infty)$ models 2004LARCH, Leverage, and Long Memory 2006Recent Advances in ARCH Modelling 2008Normalized least-squares estimation in time-varying ARCH models 2006A CLOSED-FORM ESTIMATOR FOR THE GARCH(1,1) MODEL

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