Long strange segments in a long-range-dependent moving average

Stochastic Processes and their Applications

Volumn 93, Issue 1, 2001, Pages 119-148

  T Rachev, Svetlozar ^a   Samorodnitsky, Gennady ^b  

^a UNIVERSITY OF KARLSRUHE   (Germany)

^b Cornell University ^*  (United States)

Author keywords

60F15; Applications in finance; Extreme value distribution; Heavy tails; Insurance; Large deviations; Long range dependence; Moving average process; Primary 60G10; Regular variation; Secondary 60G70; Telecommunications

Indexed keywords

EID: 0042408392     PISSN: 03044149     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0304-4149(00)00088-0     Document Type: Article

References (11)

1. Beran J. Statistics for Long-Memory Processes. 1994;Chapman and Hall, New York.
2. Bingham N., Goldie C., Teugels J. Regular Variation. 1987;Cambridge University Press, Cambridge.
3. Brockwell P., Davis R. Time Series: Theory and Methods. 2nd Edition:1991;Springer, Berlin, New York.
4. Dembo A., Zeitouni O. Large Deviations Techniques and Applications. 1993;Jones and Bartlett, Boston.
5. Hurst H. Long-term storage capacity of reservoirs. Trans. Amer. Soc. of Civ. Eng. 116:1951;770-808.
6. Karamata, J., 1962. Some theorems concerning slowly varying functions. Mathematics Research Center Technical Report No. 369, University of Wisconsin, Madison.
7. Kwapień S., Woyczyński N. Random Series and Stochastic Integrals: Single and Multiple. 1992;Birkhäuser, Boston.
8. Mansfield, P., Rachev, S., Samorodnitsky, G., 1999. Long strange segments of a stochastic process and long range dependence. Preprint. Avalilable as rareseg.ps.gz at www.orie.cornell.edu / gennady / techreports.
9. Mikosch T., Samorodnitsky G. The supremum of a negative drift random walk with dependent heavy-tailed steps. Ann. Appl. Probab. 10:2000;1025-1064.
10. Resnick S. Extreme Values, Regular Variation and Point Processes. 1987;Springer, Berlin, New York.
11. Samorodnitsky G., Taqqu M. Stable Non-Gaussian Random Processes. 1994;Chapman and Hall, New York.