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Quasi-likelihood-based higher-order spectral estimation of random fields with possible long-range dependence

Part of: Inference from stochastic processes

Published online by Cambridge University Press:  14 July 2016

V. V. Anh ,
N. N. Leonenko  and
L. M. Sakhno
V. V. Anh
Affiliation:
Program in Statistics and Operations Research, Queensland University of Technology, GPO Box 2434, Brisbane, QLD 4001, Australia. Email address: v.anh@qut.edu.au
N. N. Leonenko
Affiliation:
School of Mathematics, Cardiff University, Senghennydd Road, Cardiff CF24 4YH, UK. Email address: leonenkon@cardiff.ac.uk
L. M. Sakhno
Affiliation:
Department of Mathematics, Kyiv National Taras Shevchenko University, Volodymyrska 64, 01033, Kyiv, Ukraine. Email address: lms@univ.kiev.ua
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Abstract

This paper provides a quasi-likelihood or minimum-contrast-type method for the parameter estimation of random fields in the frequency domain based on higher-order information. The estimation technique uses the spectral density of the general kth order and allows for possible long-range dependence in the random fields. To avoid bias due to edge effects, data tapering is incorporated into the method. The suggested minimum contrast functional is linear with respect to the periodogram of kth order, hence kernel estimation for the spectral densities is not needed. Furthermore, discretization is not required in the estimation of continuously observed random fields. The consistency and asymptotic normality of the resulting estimators are established. Illustrative applications of the method to some problems in mathematical finance and signal detection are given.

Keywords

Quasi-likelihood estimationminimum contrast estimatorhigher-order spectral densitieslong-range dependence

MSC classification

Primary: 62M09: Non-Markovian processes
Secondary: 62M40: Random fields; image analysis

Information

Type
Part 2. Estimation methods
Information
Journal of Applied Probability , Volume 41 , Issue A: Stochastic Methods and their Applications , 2004 , pp. 35 - 53
Copyright
Copyright © Applied Probability Trust 2004 

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