Periodic moving averages of random variables with regularly varying tails

Annals of Statistics

Volumn 25, Issue 2, 1997, Pages 771-785

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

^a ALBION COLLEGE   (United States)

^b UNIVERSITY OF NEVADA   (United States)

Author keywords

Autocorrelation; Autocovariance; Domains of attraction; Moving average; Regular variation

Indexed keywords

EID: 0031535661     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/aos/1031833673     Document Type: Article

References (34)

1. ADAMS, G. and GOODWIN, C. (1995). Parameter estimation for periodic ARMA models. J. Time Ser. Anal. 16 127-145.
2. ANDERSON, P. and VECCHIA, A. (1993). Asymptotic results for periodic autoregressive moving-average processes. J. Time Ser. Anal. 14 1-18.
3. BHANSALI, R. (1993). Estimation of the impulse response coefficients of a linear process with infinite variance. J. Multivariate Anal. 45 274-290.
4. BILLINGSLEY, P. (1979). Probability and Measure. Wiley, New York.
5. BROCKWELL, P. and DAVIS, R. (1991). Time Series: Theory and Methods, 2nd ed. Springer, New York.
6. DAVIS, R. and RESNICK, S. (1985a). Limit theory for moving averages of random variables with regularly varying tail probabilities. Ann. Probab. 13 179-195.
7. DAVIS, R. and RESNICK, S. (1985b). More limit theory for the sample correlation function of moving averages. Stochastic Process. Appl. 20 257-279.
8. DAVIS, R. and RESNICK, S. (1986). Limit theory for the sample covariance and correlation functions of moving averages. Ann. Statist. 14 533-558.
9. FAMA, E. (1965). The behavior of stock market prices. Journal of Business 38 34-105.
10. FELLER, W. (1971). An Introduction to Probability Theory and Its Applications 2, 2nd ed. Wiley, New York.
11. GARDNER, W. and SPOONER, C. (1994). The cumulant theory of cyclostationary time-series, I: foundation. IEEE Transactions on Signal Processing 42 3387-3408.
12. HILL, B. (1975). A simple general approach to inference about the tail of a distribution. Ann. Statist. 3 1163-1173.
13. HOLTSMARK, J. (1919). Uber the Verbreiterung von Spektrallinien. Ann. Physik 58 577-630.
14. JANICKI, A. and WERON, A. (1994a). Can one see α-stable variables and processes? Statist. Sci. 9 109-126.
15. JANICKI, A. and WERON, A. (1994b). Simulation and Chaotic Behavior of α-Stable Stochastic Processes. Dekker, New York.
16. JANSEN, D. and DE VRIES, C. (1991). On the frequency of large stock market returns: putting booms and busts into perspective. Review of Economics and Statistics 23 18-24.
17. KOKOSZKA, P. (1996). Prediction of infinite variance fractional ARIMA. Probab. Math. Statist. 16 65-83.
18. KOKOSZKA, P. and TAQQU, M. (1994). Infinite variance stable ARMA processes. J. Time Ser. Anal. 15 203-220.
19. KOKOSZKA, P. and TAQQU, M. (1996). Parameter estimation for infinite variance fractional ARIMA. Ann. Statist. 24 1880-1913.
20. LOGAN, B., MALLOWS, C., RICE, S. and SHEPP, L. (1973). Limit distributions of self-normalized sums. Ann. Probab. 1 788-809.
21. LORETAN, M. and PHILLIPS, P. (1994). Testing the covariance stationarity of heavy-tailed time series. Journal of Empirical Finance 1 211-248.
22. MANDELBROT, B. (1963). The variation of certain speculative prices. Journal of Business 36 394-419.
23. k. Proc. Amer. Math. Soc. 102 341-348.
24. k. Statist. Probab. Lett. 18 233-239.
25. MIKOSCH, T., GADRICH, T., KLÜPPENBERG, C. and ADLER, R. (1995). Parameter estimation for ARMA models with infinite variance innovations. Ann. Statist. 23 305-326.
26. MITTNIK, S. and RACHEV, S. (1995). Modelling Financial Assets with Alternative Stable Models. Wiley, New York.
27. RESNICK, S. and STǍRICǍ, C. (1995). Consistency of Hill's estimator for dependent data. J. Appl. Probab. 32 139-167.
28. RYBIN, A. K. (1978). Effectiveness and stability of estimates of the parameters of a strong signal in the case of non-Gaussian noises. Engineering Cybernetics 16 115-129.
29. SAMORODNITSKY, G. and TAQQU, M. (1994). Stable Non-Gaussian Random Processes: Stochastic Models with Infinite Variance. Chapman and Hall, London.
30. STUCK, B. W. and KLEINER, B. (1974). A statistical analysis of telephone noise. Bell System Technical Journal 53 1263-1320.
31. TAYLOR, S. (1986). Modelling Financial Time Series. Wiley, New York.
32. TIAO, G. and GRUPE, M. (1980). Hidden periodic autoregressive-moving average models in time series data. Biometrika 67 365-373.
33. TJOSTHEIM, D. and PAULSEN, J. (1982). Empirical identification of multiple time series. J. Time Ser. Anal. 3 265-282.
34. ULA, T. (1993). Forecasting of multivariate periodic autoregressive moving-average processes. J. Time Ser. Anal. 14 645-657.