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The Cumulant Generating Function Estimation Method

Implementation and Asymptotic Efficiency

Published online by Cambridge University Press:  11 February 2009

John L. Knight  and
Stephen E. Satchell
John L. Knight
Affiliation:
University of Western Ontario
Stephen E. Satchell
Affiliation:
Trinity College
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Abstract

This paper deals with the use of the empirical cumulant generating function to consistently estimate the parameters of a distribution from data that are independent and identically distributed (i.i.d.). The technique is particularly suited to situations where the density function is unknown or unbounded in parameter space. We prove asymptotic equivalence of our technique to that of the empirical characteristic function and outline a six-step procedure for its implementation. Extensions of the approach to non-i.i.d. situations are considered along with a discussion of suitable applications and a worked example.

Type
Articles
Information
Econometric Theory , Volume 13 , Issue 2 , April 1997 , pp. 170 - 184
Copyright
Copyright © Cambridge University Press 1997

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References

REFERENCES

Feuerverger, A. (1990) An efficiency result for the empirical characteristic function in stationary time series models. Canadian Journal of Statistics 18, 155–161.CrossRefGoogle Scholar
Feuerverger, A. & McDunnough, P. (1981a) On some Fourier methods for inference. Journal of the American Statistical Association 76, 379–387.CrossRefGoogle Scholar
Feuerverger, A. & McDunnough, P. (1981b) On the efficiency of the empirical characteristic function procedures. Journal of the Royal Statistical Society, Series B 43, 20–27.Google Scholar
Feuerverger, A. & Mureika, R. (1977) The empirical characteristic function and its applications. Annals of Statistics 5, 88–97.CrossRefGoogle Scholar
Jorion, P. (1988) On jump processes in the foreign exchange and stock markets. Review of Financial Studies 1, 427–445.CrossRefGoogle Scholar
Knight, J.L. & Satchell, S.E. (1993) GARCH Processes–Via Compound Poisson Processes. Mimeo, University of Western Ontario.Google Scholar
Knight, J.L. & Satchell, S.E. (1994)). Estimation of stationary stochastic processes via the empirical characteristic function. Mimeo, University of Western Ontario, London, Ontario.Google Scholar
Quandt, R. & Ramsey, J. (1978) Estimating mixtures of Normal distributions and switching regressions. Journal of the American Statistical Association 73, 730–738.Google Scholar
Schmidt, P. (1982) An improved version of the Quandt-Ramsey mgf estimator for mixtures of Normal distributions and switching regressions. Econometrica 50, 501–516.CrossRefGoogle Scholar