Modeling river flows with heavy tails

Water Resources Research

Volumn 34, Issue 9, 1998, Pages 2271-2280

  Anderson, Paul L ^a   Meerschaert, Mark M ^b  

^a ALBION COLLEGE   (United States)

^b UNIVERSITY OF NEVADA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

MODELING; RIVER FLOW; TIME SERIES ANALYSIS;

UNITED STATES, ARIZONA, SALT RIVER;

EID: 0031713724     PISSN: 00431397     EISSN: None     Source Type: Journal    
DOI: 10.1029/98WR01449     Document Type: Article

References (34)

1. Adams, G., and C. Goodwin, Parameter estimation for periodic ARMA models, J. Time Ser. Anal., 16, 127-145, 1995.
2. Anderson, P., and M. Meerschaert, Periodic moving averages or random variables with regularly varying tails, Ann. Stat., 25, 771-785, 1997.
3. Anderson, P., and A. Vecchia, Asymptotic results for periodic autoregressive moving-average processes, J. Time Ser. Anal., 14, 1-18, 1993.
4. Bhansali, R., Estimation of the impulse response coefficients of a linear process with infinite variance, J. Multivariate Anal., 45, 274-290, 1993.
5. Brockwell, P., and R. Davis, Time Series: Theory and Methods, 2nd ed., Springer-Verlag, New York, 1991.
6. Chambers, J., C. Mallows, and B. Stuck, A method for simulating stable random variables, JASA J. Am. Stat. Assoc., 71, 340-344, 1976.
7. Davis, R., and S. Resnick, Limit theory for moving averages of random variables with regularly varying tail probabilities, Ann. Probab., 13, 179-195, 1985.
8. Fama, E., The behavior of stock market prices, J. Bus., 38, 34-105, 1965.
9. Feller, W., An Introduction to Probability Theory and Its Applications, vol. 2, 2nd ed., John Wiley, New York, 1971.
10. Gardner, W., and C. Spooner, The cumulant theory of cyclostationary time-series, I, Foundation, IEEE Trans. Signal Proc., 42, 3387-3408, 1994.
11. Hall, P., On some simple estimates of an exponent of regular variation, J. R. Stat. Soc., Ser. B, 44, 37-42, 1982.
12. Hill, B., A simple general approach to inference about the tail of a distribution, Ann. Stat., 1163-1173, 1975.
13. Hosking, J. R. M., and J. R. Wallis, Parameter and quantile estimation for the generalized Pareto distribution, Technometrics, 29, 339-349, 1987.
14. Janicki, A., and A. Weron, Simulation and Chaotic Behavior of a Stable Stochastic Processes, Marcel Dekker, New York, 1994.
15. Jansen, D., and C. de Vries, On the frequency of large stock market returns: Putting booms and busts into perspective, Rev. Econ. Stat., 23, 18-24, 1991.
16. Kokoszka, P., Prediction of infinite variance fractional ARIMA, Probab. Math. Stat., 16, 65-83, 1996.
17. Kokoszka, P., and M. Taqqu, Infinite variance stable ARMA processes, J. Time Series Anal., 115, 203-220, 1994.
18. Kokoszka, P., and M. Taqqu, Parameter estimation for infinite variance fractional ARIMA, Ann. Stat., 24, 1880-1913, 1996.
19. Leadbetter, M., G. Lindgren, and H. Rootzén, Extremes and Related Properties of Random Sequences and Processes, Springer-Verlag, New York, 1980.
20. Loretan, M., and P. Phillips, Testing the covariance stationarity of heavy-tailed time series, J. Empirical Finan., 1, 211-248, 1994.
21. Mandelbrot, B., The variation of certain speculative prices, J. Bus., 36, 394-419, 1963.
22. McCulloch, J. H., Measuring tail thickness in order to estimate the stable index α: A critique, J. Bus. Econ. Stat., 15, 74-81, 1995.
23. McCulloch, J. H., and D. B. Panton, Precise tabulation of the maximally-skewed stable distributions and densities, Comput. Stat. Data Anal., 23, 307-320, 1996.
24. Meerschaert, M., and H. P. Scheffler, A simple robust estimator for the thickness of heavy tails, J. Stat. Plann. Inference, in press, 1998.
25. Mikosch, T., T. Gadrich, C. Klüppenberg, and R. Adler, Parameter estimation for ARMA models with infinite variance innovations, Ann. Stat., 23, 305-326, 1995.
26. Mittnik, S., and S. Rachev, Modelling Financial Assets with Alternative Stable Models, John Wiley, New York, 1995.
27. Nikias, C., and M. Shao, Signal Processing With Alpha Stable Distributions and Applications, John Wiley, New York, 1995.
28. Resnick, S., and C. Stǎricǎ, Consistency of Hill's estimator for dependent data, J. Appl. Probab., 32, 139-167, 1995.
29. Samorodnitsky, G., and M. Taqqu, Stable Non-Gaussian Random Processes: Stochastic Models With Infinite Variance, Chapman and Hall, New York, 1994.
30. Smith, R. L., Threshold methods for sample extremes: Statistical extremes and applications (Vimeiro, 1983), NATO ASI Ser. Ser. C, D. Reidel, Norwell, Mass., 131, 621-638, 1984.
31. Tiao, G., and M. Grupe, Hidden periodic autoregressive-moving average models in time series data, Biometrika, 67, 365-373, 1980.
32. Tjostheim, D., and J. Paulsen, Empirical identification of multiple time series, J. Time Series Anal., 3, 265-282, 1982.
33. Ula, T., Forecasting of multivariate periodic autoregressive moving-average processes, J. Time Series Anal., 14, 645-657, 1993.
34. Weron, R., On the Chambers-Mallows-Stuck method for simulating skewed stable random variables, Stat. Probab. Lett., 28, 165-171, 1996.