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On the Structure and Estimation of Reflection Positive Processes

Part of: Nonparametric inference Inference from stochastic processes

Published online by Cambridge University Press:  14 July 2016

R. McVinish
R. McVinish*
Affiliation:
Queensland University of Technology
*
∗ Postal address: School of Mathematical Sciences, Queensland University of Technology, Brisbane, QLD 4001, Australia. Email address: r.mcvinish@qut.edu.au
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Abstract

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The class of processes formed as the aggregation of Ornstein-Uhlenbeck processes has proved useful in modeling time series from a number of areas and includes several interesting special cases. This paper examines the second-order properties of this class. Bounds on the one-step prediction error variance are proved and consistency of the minimum contrast estimation is demonstrated.

Keywords

Aggregationlong memoryminimum contrast estimationprediction error

MSC classification

Secondary: 62M15: Spectral analysis 62G05: Estimation

Information

Type
Research Article
Information
Journal of Applied Probability , Volume 45 , Issue 1 , March 2008 , pp. 150 - 162
Copyright
Copyright © Applied Probability Trust 2008 

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