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An Inverse Gamma Activity Time Process with Noninteger Parameters and a Self-Similar Limit

Part of: Applications Stochastic processes

Published online by Cambridge University Press:  04 February 2016

Richard Finlay ,
Eugene Seneta  and
Dingcheng Wang
Richard Finlay*
Affiliation:
University of Sydney
Eugene Seneta*
Affiliation:
University of Sydney
Dingcheng Wang*
Affiliation:
Australian National University and Nanjing Audit University
*
∗ 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.
∗∗∗∗ Email address: [email protected]
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Abstract

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We construct a process with inverse gamma increments and an asymptotically self-similar limit. This construction supports the use of long-range-dependent t subordinator models for actual financial data as advocated in Heyde and Leonenko (2005), in that it allows for noninteger-valued model parameters, as is found empirically in model estimation from data.

Keywords

Inverse gamma processt-distributionsubordinator modellong-range dependenceself similarity

MSC classification

Primary: 60G10: Stationary processes
Secondary: 60G18: Self-similar processes 62P20: Applications to economics
Type
Research Article
Information
Journal of Applied Probability , Volume 49 , Issue 2 , June 2012 , pp. 441 - 450
Copyright
© Applied Probability Trust 

References

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