Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-27T01:38:22.415Z Has data issue: false hasContentIssue false
  • English
  • Français

On dispersion of stable random vectors and its application in the prediction of multivariate stable processes

Part of: Stochastic processes

Published online by Cambridge University Press:  14 July 2016

A. Reza Soltani  and
R. Moeanaddin
A. Reza Soltani
Affiliation:
Shiraz University, Iran
R. Moeanaddin*
Affiliation:
Shiraz University, Iran
*
∗ Postal address for both authors: Department of Statistics, Faculty of Sciences, Shiraz University, Shiraz 71454, Iran.
Get access Rights & Permissions [Opens in a new window]

Abstract

Our aim in this article is to derive an expression for the best linear predictor of a multivariate symmetric α stable process based on many past values. For this purpose we introduce a definition of dispersion for symmetric α stable random vectors and choose the linear predictor which minimizes the dispersion of the error vector.

Keywords

BEST LINEAR PREDICTORMULTIVARIATE STABLE PROCESSESSPECTRAL MEASURESYMMETRIC α-STABLE ARMA PROCESSES

MSC classification

Primary: 60G25: Prediction theory
Type
Research Papers
Information
Journal of Applied Probability , Volume 31 , Issue 3 , September 1994 , pp. 691 - 699
Copyright
Copyright © Applied Probability Trust 1994 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Brockwell, P. J. and Davis, R. A. (1987) Time Series: Theory and Methods. Springer-Verlag, New York.Google Scholar
Cambanis, S. and Miller, G. (1981) Linear problems in pth order and stable processes. SIAM J. Appl. Math. 41, 43–69.Google Scholar
Cambanis, S. and Soltani, A. R. (1982) Prediction of stable processes: spectral and moving average representations. Tech. Rpt. 11, Center for Stochastic Processes, University of North Carolina, Chapel Hill.Google Scholar
Cline, D. B. H. and Brockwell, P. J. (1985) Linear prediction of ARMA processes with infinite variance. Stoch. Proc. Appl. 19, 281–296.Google Scholar
Kanter, M. (1973) The Lp norm of sums of translates of a function. Trans. Amer. Math. Soc. 197, 35–47.Google Scholar
Kuelbs, J. (1973) A representation theorem for symmetric stable processes and stable measures on H. Z. Wahrscheinlichkeitsth. 26, 259–271.Google Scholar
Paulauskas, V. J. (1976) Some remarks on multivariate stable distributions. J. Multivariate Anal. 6, 356–368.Google Scholar
Samorodnitsky, S. and Taqqu, M. S. (1991) Conditional moments and linear regression for stable random variables. Stoch. Proc. Appl. 39, 183–199.Google Scholar
Soltani, A. R. (1991) On spectral representation of multivariate stable processes. Theory Prob. Appl. To appear.Google Scholar
Soltani, A. R. (1992) More on conditional moments of stable random variables. Invited papers, First Iranian Statistical Conference, 195–201.Google Scholar
Stuck, R. (1978) Minimum error dispersion linear filtering of scalar symmetric stable processes. IEEE Trans. Autom. Control. 23, 507–509.CrossRefGoogle Scholar