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Theoretical prediction of periodically correlated sequences

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Języki publikacji
EN
Abstrakty
EN
The paper deals with a spectral analysis and prediction of periodically correlated (PC) sequences. In particular, a moving average representation of a predictor is obtained and its coefficients are described in the language of outer factors of spectral line densities of the sequence. A comprehensive and self-contained overview of the spectral theory of PC sequences is included. The developed technique is used to compute the spectrum and an optimal moving average representation of a PC solution to a PARMA system of equations.
Rocznik
Strony
287--322
Opis fizyczny
Bibliogr. 23 poz.
Twórcy
autor
  • Department of Mathematics, Hampton University, Hampton, VA 23668, USA
Bibliografia
  • [1] M. Bentarzi and M. Hallin, On the invertibility of periodic moving-average models, J. Time Ser. Anal. 15 (3) (1996), pp. 263-268.
  • [2] P. J. Brockwell and R. A. Davis, Time Series: Theory and Methods, Springer, 1987.
  • [3] N. Dunford and J. Schwartz, Linear Operators, Wiley, 1988.
  • [4] W. A. Gardner and L. E. Franks, Characterization of cyclostationary random processes, IEEE Trans. Inform. Theory IT-21 (1975), pp. 4-14.
  • [5] E. G. Gladyshev, Periodically correlated random sequences, Soviet Math. 2 (1961), pp. 385-388.
  • [6] - Periodically and almost periodically correlated random processes with continuous time parameter, Theory Probab. Appl, 8 (1963), pp. 173-177.
  • [7] H. L. Hurd, Periodically correlated processes with discontinuous correlation function, ibidem 19 (1974), pp. 834-838.
  • [8] - Stationarizing properties of random shifts, SIAM J. Appl. Math. 26 (1) (1974), pp. 203-211.
  • [9] - Representation of strongly harmonizable periodically correlated processes and their covariance, J. Multivariate Anal. 29 (1989), pp. 53-67.
  • [10] - and A. Makagon, Spectral analysis of completely regular periodically correlated processes, Center for Stochastic Processes, University of North Carolina at Chapel Hill, unpublished report.
  • [11] - A. Makagon and A. G. Miamee, On AR(1) models with periodic and almost periodic coefficients, preprint.
  • [12] R. B. Lund and I. V. Basawa, Recursive prediction and likelihood evaluation for periodic ARMA models, preprint.
  • [13] A. Makagon, Induced stationary process and structure of locally square integrable periodically correlated processes, Studia Math. (to appear).
  • [14] - A. G. Miamee and H. Salehi, Continuous time periodically correlated processes: spectrum and prediction, Stochastic Process. Appl. 49 (1994), pp. 277-295.
  • [15] - Periodically correlated processes and their spectrum, in: Nonstationary Stochastic Processes and Their Applications, A. G. Miamee (Ed,), Word Scientific, 1991, pp. 147-164.
  • [16] A. Makagon and H. Salehi, Notes on infinite dimensional stationary sequences, in: Probability Theory on Vector Spaces. IV, A. Weron (Ed.), Lecture Notes in Math. 1391, Springer, 1989, pp. 200-238.
  • [17] Structure of periodically distributed stochastic sequences, in: Stochastic Processes. A Festschrift in Honour of Dopinath Kallianpur, S. Cambanis (Ed.), Springer, 1993, pp. 245-251.
  • [18] P. Masani, Recent trends in multivariate prediction theory, in: Multivariate Analysis, P. R. Krishnaiah (Ed.), Proc. International Symp. Dayton, Ohio 1965, Academic Press 1966, pp. 351-382.
  • [19] A. G. Miamee, Explicit formula for the best linear predictor of periodically correlated sequences, SIAM J. Math. Anal. 24 (1993), pp. 703-711.
  • [20] - and H. Salehi, On the prediction of periodically correlated stochastic process, in: Multivariate Analysis. V, P. R. Krishnaiah (Ed.), North-Holland, Amsterdam 1980, pp. 167-179.
  • [21] M. Pagano, On periodic and multiple autoregression, Ann. Statist. 6 (1978), pp. 1310-1317.
  • [22] H. Sakai, On the spectral density matrix of a periodic ARMA process, J. Time Ser. Anal. 12 (1991), pp. 72-82.
  • [23] A. V. Vecchia, Periodic Autoregressive Moving Average (PARMA) modeling with applications to water resources, Water Resources Bulletin 21 (5) (1985), pp. 721-730.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-159a4dd1-a817-4eec-9a50-f6c6a5b3c178
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