Hostname: page-component-586b7cd67f-2brh9 Total loading time: 0 Render date: 2024-11-22T04:24:05.212Z Has data issue: false hasContentIssue false
  • English
  • Français

Stable Non-Gaussian Random ProcessesGennady Samorodnitsky and Murad S. Taqqu Chapman and Hall, 1994

Published online by Cambridge University Press:  11 February 2009

Keith Knight
Keith Knight
Affiliation:
University of Toronto
Get access Rights & Permissions [Opens in a new window]

Abstract

An abstract is not available for this content so a preview has been provided. Please use the Get access link above for information on how to access this content.
Image of the first page of this content. For PDF version, please use the ‘Save PDF’ preceeding this image.'
Type
Book Reviews
Information
Econometric Theory , Volume 13 , Issue 1 , February 1997 , pp. 133 - 142
Copyright
Copyright © Cambridge University Press 1997

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

REFERENCES

Avram, F. & Taqqu, M. (1992) Weak convergence of sums of moving averages in the α-stable domain of attraction. Annals of Probability 20, 483–503.CrossRefGoogle Scholar
Beran, J., Sherman, R., Taqqu, M.S., & Willinger, W. (1995) Long-range dependence in variablebit- rate video traffic. IEEE Transactions on Communications 43, 1566–1579.CrossRefGoogle Scholar
Beveridge, S. & Nelson, C.R. (1981) A new approach to decomposition of economic time series into permanent and transitory components with particular attention to measurement of the “business cycle.” Journal of Monetary Economics 7, 151–174.CrossRefGoogle Scholar
Christoph, G. & Wolf, W. (1992) Convergence Theorems with a Stable Limit Law. Berlin: Akademie-Verlag.Google Scholar
Davis, R.A., Knight, K., & Liu, J. (1992) M-estimation for autoregressions with infinite variance. Stochastic Processes and Their Applications 14, 533–558.Google Scholar
Davis, R.A. & Resnick, S. (1985) Limit theory for moving averages of random variables with regularly varying tail probabilities. Annals of Probability 13, 179–195.CrossRefGoogle Scholar
Duffy, D.E., Mclntosh, A., Rosenstein, M., & Willinger, W. (1994) Statistical analysis of CCSN/SS7 traffic data from working subnetworks. IEEE Journal of Selected Areas in Communications 12, 544–551.CrossRefGoogle Scholar
Fama, E.F. (1965) The behavior of stock market prices. Journal of Business 38, 34–105.CrossRefGoogle Scholar
Feller, W. (1971) An Introduction to Probability Theory and Its Applications, vol. 2, 2nd ed. New York: Wiley.Google Scholar
Hill, B. (1975) A simple general approach to inference about the tail of a distribution. Annals of Statistics 3, 1163–1174.CrossRefGoogle Scholar
Janicki, A. & Weron, A. (1993) Simulation and Chaotic Behavior of α-Stable Stochastic Processes. New York: Marcel Dekker.Google Scholar
Kanter, M. & Steiger, W.L. (1974) Regression and autoregression with infinite variance. Advances in Applied Probability 6, 768–783.CrossRefGoogle Scholar
Knight, K. (1991) Limit theory for M-estimates in an integrated infinite variance process. Econometric Theory 7, 200–212.CrossRefGoogle Scholar
Lau, A.H.L., Lau, H.S., & Wingender, J.R. (1990) The distribution of stock returns: New evidence against the stable model. Journal of Business and Economic Statistics 8, 217–223.CrossRefGoogle Scholar
Lepage, R., Woodroofe, M., and Zinn, J. (1981) Convergence to a stable law via order statistics. Annals of Probability 9, 624–632.CrossRefGoogle Scholar
Mandelbrot, B. (1963) The variation of certain speculative prices. Journal of Business 36, 394–419.CrossRefGoogle Scholar
Mandelbrot, B. (1967) The variation of some other speculative prices. Journal of Business 40, 393–413.CrossRefGoogle Scholar
Mantegna, R.S. & Stanley, H.E. (1995) Scaling behaviour in the dynamics of an economic index. Nature 376, 46–49.CrossRefGoogle Scholar
Mikosch, T., Gadrich, T., Klüppelberg, C., & Adler, R.J. (1995) Parameter estimation for ARMA models with infinite variance innovations. Annals of Statistics 23, 282–304.CrossRefGoogle Scholar
Phillips, P.C.B. (1990) Time series regression with a unit root and infinite variance errors. Econometric Theory 6, 44–62.CrossRefGoogle Scholar
Phillips, P.C.B. & Solo, V. (1992) Asymptotics for linear processes. Annals of Statistics 20, 971–1001.CrossRefGoogle Scholar
Pollard, D. (1984) Convergence of Stochastic Processes. New York: Springer.CrossRefGoogle Scholar
Samorodnitsky, G. & Taqqu, M.S. (1994) Stable Non-Gaussian Random Processes: Stochastic Models with Infinite Variance. New York: Chapman-Hall.Google Scholar
Skorokhod, A. V. (1956) Limit theorems for stochastic processes. Theory of Probability and Its Applications 1, 261–290.CrossRefGoogle Scholar
Willinger, W., Taqqu, M.S., Leland, W.E., & Wilson, D.V. (1995) Self-similarity in high-speed packet traffic: Analysis and modeling of Ethernet traffic measurements. Statistical Science 10, 67–85.CrossRefGoogle Scholar
Willinger, W., Taqqu, M.S., Sherman, R., & Wilson, D.V. (1995) Self-similarity through highvariability: Statistical analysis of Ethernet LAN traffic at the source level. Computer Communication Review 25, 100–113.CrossRefGoogle Scholar
Zolotarev, V.M. (1986) One-Dimensional Stable Distributions. Providence, Rhode Island: American Mathematical Society.CrossRefGoogle Scholar