Empirical Characteristic Function in Time Series Estimation
University of Western Ontario - Department of Economics
Singapore Management University
April 20, 2001
Auckland Department of Economics Working Paper No. 200
Since 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 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.
Number of Pages in PDF File: 41
Keywords: Empirical Characteristic Function, Stationary Processes, Gaussian ARMA Processes, Stable ARMA Processes
JEL Classification: C13, C15, C22working papers series
Date posted: May 1, 2001
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