Recursive prediction and likelihood evaluation for periodic ARMA models

Journal of Time Series Analysis

Volumn 21, Issue 1, 2000, Pages 75-93

  Lund, Robert ^a   Basawa, I V ^a  

^a UNIVERSITY OF GEORGIA   (United States)

Author keywords

Innovations algorithm; Likelihood evaluation; Mean squared error; Multivariate ARMA models; Prediction

Indexed keywords

EID: 0002518113     PISSN: 01439782     EISSN: None     Source Type: Journal    
DOI: 10.1111/1467-9892.00174     Document Type: Article

References (26)

1. ADAMS, G. J. and GOODWIN, G. C. (1995) Parameter estimation for periodic ARMA models. J. Time Ser. Anal. 16, 127-46.
2. ANDERSON, P. L. and VECCHIA, A. V. (1983) Asymptotic results for periodic autoregressive moving-average processes. J. Time Ser. Anal. 14, 1-18.
3. ANSLEY, C. F. (1979) An algorithm for the exact likelihood of a mixed autoregressive moving-average process. Biometrika 66, 59-65.
4. BENTARZI, M. and HALLIN, M. (1993) On the invertibility of periodic moving-average models. J. Time Ser. Anal. 15, 263-68.
5. BLOOMFIELD, P., HURD, H. L. and LUND, R. B. (1994) Periodic correlation in stratospheric ozone data. J. Time Ser. Anal 15, 127-50.
6. Box, G. E. P., JENKINS, G. M. and REINSEL, G. C. (1994) Time Series Analysis. Forecasting and Control, 3rd Edn. Englewood Cliffs, NJ: Prentice Hall.
7. BROCKWELL, P. J. and DAVIS, R. A. (1991) Time Series: Theory and Methods, 2nd Edn. New York: Springer.
8. CIPRA, T. and TLUSTÝ, P. (1987) Estimation in multiple autoregressive-moving average models using periodicity. J. Time Ser. Anal. 8, 293-300.
9. GARDNER, W. and FRANKS, L. E. (1975) Characterization of cyclostationary random signal processes. IEEE Trans. Inf. Theory 21, 4-14.
10. GLADYŠHEV, E. G. (1961) Periodically correlated random sequences. Sov. Math. 2, 385-88.
11. HALLIN, M. and INGENBLEEK, J. (1983) Nonstationary Yule-Walker equations. Stat. Probab. Lett. 1, 189-95.
12. HANNAN, E. J. (1955) A test for singularities in Sydney rainfall. Aust. J. Phys. 8, 289-97.
13. JONES, R. H. and BRELSFORD, W. M. (1967) Time series with periodic structure. Biometrika 54, 403-8.
14. LAWRANCE, A. J. and KOTTEGODA, N. T. (1977) Stochastic modeling of river flow time series. J. R. Stat. Soc., Ser. A 140, 1-31.
15. LI, W. K. and HUI, Y. V. (1988) An algorithm for the exact likelihood of periodic autoregressive moving average models. Commun. Stat., Simulation Comput. 17, 1483-94.
16. LUND, R. B. and BASAWA, I. V. (1999) Modeling and inference for periodically correlated time series. Asymptotics, Nonparametrics, and Time Series (ed. S. Ghosh), 37-62. Marcel Dekker, New York.
17. _, HURD, H. L., BLOOMFIELD, P. and SMITH, R. L. (1995) Climatological time series with periodic correlation. J. Clim. 11, 2787-809.
18. MAURICIO, J. A. (1997) The exact likelihood function of a vector autoregressive moving-average model. Appl. Stat., Ser. C 46, 157-71.
19. MONIN, A. S. (1963) Stationary and periodic time series in the general circulation of the atmosphere. In Proceedings, Symposium on Time Series Analysis (ed. M. Rosenblatt), pp. 144-51. John Wiley & Sons, NewYork.
20. MCLEOD, A. I. (1993) Parsimony, model adequacy and periodic correlation in time series forecasting. Int. Stat. Rev. 61, 387-93.
21. PARZEN, E. and PAGANO, M. (1979) An approach to modeling seasonally stationary time series. J. Economet. 9, 137-53.
22. THOMPSTONE, R. M., HIPEL, K. W. and MCLEOD, A. I. (1985) Grouping of periodic autoregressive models. In Time Series Analysis: Theory and Practice, Vol. 6 (eds O. D. Anderson, J. K. Ord and E. A. Robinson). Amsterdam: Elsevier, pp. 35-49.
23. ULA, T. A. (1993) Forecasting of multivariate periodic autoregressive moving-average processes. J. Time Ser. Anal. 14, 645-57.
24. VECCHIA, A. V. (1985a) Periodic autoregressive-moving average (PARMA) modeling with applications to water resources. Water Resour. Bull. 21, 721-30.
25. _ (1985b) Maximum likelihood estimation for periodic autoregressive moving average models. Technometrics 27, 375-84.
26. _ (1997) Parameter estimation for multivariate periodic ARMA models. Preprint.