EMPIRICAL CHARACTERISTIC FUNCTION IN TIME SERIES ESTIMATION

Because the empirical characteristic function (ECF) is the Fourier transform of the empirical distribution function, it retains all the information in the sample but can overcome difficulties arising from the likelihood. This paper discusses an estimation method via the ECF for strictly stationary p...

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Bibliographic Details
Published in:	Econometric theory 2002-06, Vol.18 (3), p.691-721
Main Authors:	Knight, John L., Yu, Jun
Format:	Article
Language:	eng
Subjects:	Autoregressive moving average Consistent estimators Econometrics Economic models Eigenfunctions Estimation Estimation methods Estimators Fourier transforms Generalized method of moments Information Interest Literature reviews Maximum likelihood estimation Methods Modeling Parameter estimation Parametric models Stochastic models Time series Weighting functions
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Summary:	Because the empirical characteristic function (ECF) is the Fourier transform of the empirical distribution function, it retains all the information in the sample but can overcome difficulties arising from the likelihood. This paper discusses an estimation method via the ECF for strictly stationary processes. Under some regularity conditions, the resulting estimators are shown to be consistent and asymptotically normal. The method is applied to estimate the stable autoregressive moving average (ARMA) models. For the general stable ARMA model for which the maximum likelihood approach is not feasible, Monte Carlo evidence shows that the ECF method is a viable estimation method for all the parameters of interest. For the Gaussian ARMA model, a particular stable ARMA model, the optimal weight functions and estimating equations are given. Monte Carlo studies highlight the finite sample performances of the ECF method relative to the exact and conditional maximum likelihood methods.
ISSN:	0266-4666 1469-4360