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A Gamma Activity Time Process with Noninteger Parameter and Self-Similar Limit

Part of: Applications Stochastic processes

Published online by Cambridge University Press:  14 July 2016

Richard Finlay  and
Eugene Seneta
Richard Finlay*
Affiliation:
University of Sydney
Eugene Seneta*
Affiliation:
University of Sydney
*
∗Postal address: School of Mathematics and Statistics F07, University of Sydney, NSW 2006, Australia.
∗Postal address: School of Mathematics and Statistics F07, University of Sydney, NSW 2006, Australia.
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Abstract

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We construct a process with gamma increments, which has a given convex autocorrelation function and asymptotically a self-similar limit. This construction validates the use of long-range dependent t and variance-gamma subordinator models for actual financial data as advocated in Heyde and Leonenko (2005) and Finlay and Seneta (2006), in that it allows for noninteger-valued model parameters to occur as found empirically by data fitting.

Keywords

Gamma processvariance-gamma distributiont distributionsubordinator modelconstructionlong-range dependenceself-similarity

MSC classification

Secondary: 60G10: Stationary processes 60G18: Self-similar processes 62P20: Applications to economics
Type
Research Papers
Information
Journal of Applied Probability , Volume 44 , Issue 4 , December 2007 , pp. 950 - 959
Copyright
Copyright © Applied Probability Trust 2007 

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