Innovations algorithm for periodically stationary time series

Stochastic Processes and their Applications

Volumn 83, Issue 1, 1999, Pages 149-169

  Anderson, Paul L ^a   Meerschaert, Mark M ^a   Vecchia, Aldo V ^b  

^a UNIVERSITY OF NEVADA   (United States)

^b NONE

Author keywords

60F05; 62E20; Heavy tails; Innovations algorithm; Periodically stationary; Primary 62M10; Regular variation; Secondary 60E07; Time series; Yule Walker estimates

Indexed keywords

EID: 0000627355     PISSN: 03044149     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0304-4149(99)00027-7     Document Type: Article

References (29)

1. Adams G., Goodwin C. Parameter estimation for periodic ARMA models. J. Time Ser. Anal. 16:1995;127-145.
2. Anderson, P., 1989. Asymptotic results and identification for cyclostationary times series. Doctoral Dissertation, Colorado School of Mines, Golden, Colorado.
3. Anderson P., Meerschaert M. Modeling river flows with heavy tails. Water Resources Res. 34:1998;2271-2280.
4. Anderson P., Meerschaert M. Periodic moving averages of random variables with regularly varying tails. Ann. Statist. 25:1997;771-785.
5. Anderson, P., Meerschaert, M., Vecchia, A., 1998. Asymptotics of the innovations algorithm for periodic time series, in preparation.
6. Anderson P., Vecchia A. Asymptotic results for periodic autoregressive moving-average processes. J. Time Ser. Anal. 14:1993;1-18.
7. Berk K. Consistent autoregressive spectral estimates. Ann. Statist. 2:1974;489-502.
8. Bhansali R. Linear prediction by autoregressive model fitting in the time domain. Ann. Statist. 6:1978;224-231.
9. Billingsley, 1968. Convergence of Probability Measures. Wiley, New York.
10. Billingsley, 1995. Probability and Measure, 3rd Edition. Wiley, New York.
11. Bingham, N., Goldie, C., Teugels, J., 1987. Regular variation. Encyclopedia of Mathematics and its Applications, vol. 27. Cambridge University Press, Cambridge.
12. Brockwell P., Davis R. Simple consistent estimation of the coefficients of a linear filter. Stochastic Process Appl. 28:1988;47-59.
13. Brockwell, P., Davis, R., 1991. Time Series: Theory and Methods, 2nd Edition. Springer, New York.
14. Davis R., Resnick S. Limit theory for the sample covariance and correlation functions of moving averages. Ann. Statist. 14:1986;533-558.
15. Feller, W., 1971. An Introduction to Probability Theory and Its Applications, Vol. II, 2nd Edition. Wiley, New York.
16. Golub, G., Van Loan, C., 1989. Matrix Computations, 2nd Edition, Johns Hopkins University Press, Baltimore, MA.
17. Jansen D., de Vries C. On the frequency of large stock market returns: Putting booms and busts into perspective. Review Econom. Statist. 23:1991;18-24.
18. Jones R., Brelsford W. Time series with periodic structure. Biometrika. 54:1967;403-408.
19. Loretan, M., Phillips, P., 1994. Testing the covariance stationarity of heavy-tailed time series, J. Empirical Finance 1, 211-248.
20. Lund, R., Basawa, I., 1999. Recursive Prediction and Likelihood Evaluation for Periodic ARMA Models. J. Time Ser. Anal., to appear.
21. Mikosch T., Gadrich T., Klüppenberg C., Adler R. Parameter estimation for ARMA models with infinite variance innovations. Ann. Statist. 23:1995;305-326.
22. Pagano M. On periodic and multiple autoregressions. Ann. Statist. 6:1978;1310-1317.
23. Salas J., Tabios G., Bartolini P. Approaches to multivariate modeling of water resources time series. Water Res. Bull. 21:1985;683-708.
24. Samorodnitsky, G., Taqqu, M., 1994. Stable non-Gaussian Random Processes: Stochastic Models with Infinite Variance. Chapman & Hall, London.
25. Tiao G., Grupe M. Hidden periodic autoregressive-moving average models in time series data. Biometrika. 67:1980;365-373.
26. Tjostheim D., Paulsen J. Empirical identification of multiple time series. J. Time Ser. Anal. 3:1982;265-282.
27. Troutman B. Some results in periodic autoregression. Biometrika. 6:1979;219-228.
28. Ula T. Forecasting of multivariate periodic autoregressive moving average processes. J. Time Ser. Anal. 14:1993;645.
29. Vecchia A., Ballerini R. Testing for periodic autocorrelations in seasonal time series data. Biometrika. 78:1991;53-63.