Chebyshev Polynomial Approximations and Characteristic Function Estimation

Abstract

SUMMARY A new procedure for estimating characteristic functions based on a Chebyshev polynomial expansion for the density of the Cosine is developed. Simulation results confirm the usefulness of the method. It is applied to the estimation of two stochastic process models for daily stock returns. The Press compound events model is also estimated by maximum likelihood methods. Results are suggestive of the adequacy of the compound events model and the vg model (a variant of the Praetz t distribution), and the superiority of these models over the normal and symmetric stable.

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