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

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 (...

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Bibliographic Details
Published in:Journal of applied probability 2007-12, Vol.44 (4), p.950-959
Main Authors: Finlay, Richard, Seneta, Eugene
Format: Article
Language:English
Subjects:
60G10
60G18
62P20
Applications
Asymptotic methods
Autocorrelation
construction
Correlations
Data analysis
Exact sciences and technology
Gamma process
Integers
Linear inference, regression
long-range dependence
Markovs inequality
Mathematical functions
Mathematics
Probability and statistics
Random variables
Research Papers
Sciences and techniques of general use
self-similarity
Stationary processes
Statistics
Studies
subordinator model
t distribution
variance-gamma distribution
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Description
Summary: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.
ISSN:0021-9002
1475-6072
DOI:10.1239/jap/1197908816