Empirical Characteristic Function in Time Series Estimation

Auckland Department of Economics Working Paper No. 200

41 Pages Posted: 1 May 2001

See all articles by John Knight

John Knight

University of Western Ontario, Faculty of Social Science, Deparment of Economics (Deceased)

Jun Yu

Singapore Management University - School of Economics; Singapore Management University - Lee Kong Chian School of Business

Date Written: April 20, 2001

Abstract

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.

Keywords: Empirical Characteristic Function, Stationary Processes, Gaussian ARMA Processes, Stable ARMA Processes

JEL Classification: C13, C15, C22

Suggested Citation

Knight, John L. and Yu, Jun, Empirical Characteristic Function in Time Series Estimation (April 20, 2001). Auckland Department of Economics Working Paper No. 200, Available at SSRN: https://ssrn.com/abstract=267490 or http://dx.doi.org/10.2139/ssrn.267490

John L. Knight

University of Western Ontario, Faculty of Social Science, Deparment of Economics (Deceased)

Jun Yu (Contact Author)

Singapore Management University - School of Economics ( email )

90 Stamford Road
178903
Singapore
+6568280858 (Phone)
+6568280833 (Fax)

HOME PAGE: http://www.mysmu.edu/faculty/yujun/

Singapore Management University - Lee Kong Chian School of Business ( email )

469 Bukit Timah Road
Singapore 912409
Singapore

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