Parameter estimation of selfsimilarity exponents
The characteristic feature of operator selfsimilar stochastic processes is that a linear rescaling in time is equal in the sense of distributions to a linear operator rescaling in space, which in turn is characterized by the selfsimilarity exponent. The growth behaviour of such processes in any radial direction is determined by the real parts of the eigenvalues of the selfsimilarity exponent. We extend an estimation method of Meerschaert and Scheffler [M.M. Meerschaert, H.-P. Scheffler, Moment estimator for random vectors with heavy tails, J. Multivariate Anal. 71 (1999) 145-159, M.M. Meerschaert, H.-P. Scheffler, Portfolio modeling with heavy tailed random vectors, in: S.T. Rachev (Ed.), Handbook of Heavy Tailed Distributions in Finance, Elsevier Science B.V., Amsterdam, 2003, pp. 595-640] to be applicable for estimating the real parts of the eigenvalues of the selfsimilarity exponent and corresponding spectral directions given by the eigenvectors. More generally, the results are applied to operator semi-selfsimilar processes, which obey a weaker scaling property, and to certain Ornstein-Uhlenbeck type processes connected to operator semi-selfsimilar processes via Lamperti's transformation.
Year of publication: |
2008
|
---|---|
Authors: | Becker-Kern, Peter ; Pap, Gyula |
Published in: |
Journal of Multivariate Analysis. - Elsevier, ISSN 0047-259X. - Vol. 99.2008, 1, p. 117-140
|
Publisher: |
Elsevier |
Keywords: | Operator semi-selfsimilar process Ornstein-Uhlenbeck type process Parameter estimation Selfsimilarity exponent Spectral decomposition |
Saved in:
Online Resource
Saved in favorites
Similar items by person
-
Random integral representation of operator-semi-self-similar processes with independent increments
Becker-Kern, Peter, (2004)
-
Change detection in the Cox–Ingersoll–Ross model
Pap, Gyula, (2016)
-
Forecasting Hungarian mortality rates using the Lee-Carter method
Baran, Sándor, (2007)
- More ...