Orthogonal Expansion of Levy Process Functionals: Theory and Practice

Chaohua Dong () and Jiti Gao

No 3/13, Monash Econometrics and Business Statistics Working Papers from Monash University, Department of Econometrics and Business Statistics

Abstract: In this paper, expansions of functionals of Levy processes are established under some Hilbert spaces and their orthogonal bases. From practical standpoint, both time-homogeneous and time-inhomogeneous functionals of Levy processes are considered. Several expansions and rates of convergence are established. In order to state asymptotic distributions for statistical estimators of unknown parameters involved in a general regression model, we develop a general asymptotic theory for partial sums of functionals of Levy processes. The results show that these estimators of the unknown parameters in different situations converge to quite different random variables. In addition, the rates of convergence depend on various factors rather than just the sample size. Simulations and empirical study are provided to illustrate the theoretical results.

Keywords: Asymptotic theory Expansion; Levy Process; Nonstationary time series; Orthogonal Series (search for similar items in EconPapers)
Date: 2013
New Economics Papers: this item is included in nep-ecm and nep-ets
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