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Linnik distributions and processes

Part of: Stochastic processes Inference from stochastic processes

Published online by Cambridge University Press:  14 July 2016

Dale N. Anderson  and
Barry C. Arnold
Dale N. Anderson
Affiliation:
University of California, Riverside
Barry C. Arnold*
Affiliation:
University of California, Riverside
*
∗Postal address: Department of Statistics, University of California, Riverside, CA 92521, USA.
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Abstract

Using a simple characterization of the Linnik distribution, discrete-time processes having a stationary Linnik distribution are constructed. The processes are structurally related to exponential processes introduced by Arnold (1989), Lawrance and Lewis (1981) and Gaver and Lewis (1980). Multivariate versions of the processes are also described. These Linnik models appear to be viable alternatives to stable processes as models for temporal changes in stock prices.

Keywords

GEOMETRIC COMPOUNDINGTIME SERIESSTABLE DISTRIBUTIONSTOCK PRICES

MSC classification

Primary: 60G10: Stationary processes
Secondary: 62M99: None of the above, but in this section
Type
Research Papers
Information
Journal of Applied Probability , Volume 30 , Issue 2 , June 1993 , pp. 330 - 340
Copyright
Copyright © Applied Probability Trust 1993 

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