An inverse gamma activity time process with noninteger parameters and a self-similar limit

An inverse gamma activity time process with noninteger parameters and a self-similar limit

Richard Finlay, Eugene Seneta, and Dingcheng Wang

Source: J. Appl. Probab. Volume 49, Number 2 (2012), 441-450.

Abstract

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.

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Primary Subjects: 60G10

Secondary Subjects: 60G18, 62P20

Keywords: Inverse gamma process; t-distribution; subordinator model; long-range dependence; self similarity

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Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.jap/1339878797
Digital Object Identifier: doi:10.1239/jap/1339878797
Zentralblatt MATH identifier: 06053722
Mathematical Reviews number (MathSciNet): MR2977806

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References

Finlay, R. and Seneta, E. (2006). Stationary-increment Student and variance-gamma processes. J. Appl. Prob. 43, 441–453. (Correction: 43 (2006), 1207.)

Mathematical Reviews (MathSciNet): MR2248575

Digital Object Identifier: doi:10.1239/jap/1152413733

Project Euclid: euclid.jap/1152413733

Finlay, R. and Seneta, E. (2007). A gamma activity time process with noninteger parameter and self-similar limit. J. Appl. Prob. 44, 950–959.

Mathematical Reviews (MathSciNet): MR2382937

Digital Object Identifier: doi:10.1239/jap/1197908816

Project Euclid: euclid.jap/1197908816

Finlay, R., Fung, T. and Seneta, E. (2011). Autocorrelation functions. Internat. Statist. Rev. 79, 255–271.

Gneiting, T. (2000). Power-law correlations, related models for long-range dependence and their simulation. J. Appl. Prob. 37, 1104–1109.

Mathematical Reviews (MathSciNet): MR1808873

Digital Object Identifier: doi:10.1239/jap/1014843088

Project Euclid: euclid.jap/1014843088

Griffiths, R. C. (1969). The canonical correlation coefficients of bivariate gamma distributions. Ann. Math. Statist. 40, 1401–1408.

Mathematical Reviews (MathSciNet): MR243654

Digital Object Identifier: doi:10.1214/aoms/1177697511

Project Euclid: euclid.aoms/1177697511

Heyde, C. C. and Leonenko, N. N. (2005). Student processes. Adv. Appl. Prob. 37, 342–365.

Mathematical Reviews (MathSciNet): MR2144557

Digital Object Identifier: doi:10.1239/aap/1118858629

Project Euclid: euclid.aap/1118858629

Leonenko, N. (1999). Limit Theorems for Random Fields with Singular Spectrum. Kluwer, Dordrecht.

Mathematical Reviews (MathSciNet): MR1687092

Leonenko, N. N., Petherick, S. and Sikorskii, A. (2012). Fractal activity time models for risky asset with dependence and generalized hyperbolic distributions. Stoch. Anal. Appl. 30, 476–492.

Taqqu, M. S. (1975). Weak convergence to fractional Brownian motion and to the Rosenblatt process. Z. Wahrscheinlichkeitsth. 31, 287–302. \endharvreferences

Mathematical Reviews (MathSciNet): MR400329

Digital Object Identifier: doi:10.1007/BF00532868

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