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On PC solutions of PARMA (p, q) models

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Języki publikacji
EN
Abstrakty
EN
This note is concerned with the existence of periodically correlated solutions for the PARMA (p, q) system xn = φ1n xn – 1 + φ2n xn – 2 +...+ φpn xn – p + ξn + θ1n ξn-1… + θqn ξn-q, n ∈ Z, where ξn is a white noise and the varying coefficients φin and θin are periodic in n with period T. Conditions which ensure the existence of periodically correlated solutions for such systems are obtained.
Słowa kluczowe
Rocznik
Strony
279--288
Opis fizyczny
Bibliogr. 16 poz.
Twórcy
autor
  • Department of Mathematics, Hampton University, Hampton VA, 23668 U.S.A.
autor
  • Department of Mathematics, Pyam-e Nour University, Mashad, Iran
Bibliografia
  • [1] P. L. Anderson, M. M. Meerschaert and A. V. Vecchia, Innovation algorithm for periodically stationary time series, Stochastic Process. Appl. 83 (1999), pp. 149-169.
  • [2] M. Bentarzi and M. Hallin, On the invertibility of periodic moving average models, J. Time Ser. Anal. 15 (1994), pp. 263-268.
  • [3] P. Bloomfield, H. Hurd and R. Lund, Periodic correlation in stratospheric ozone time series, J. Time Ser. Anal. 15 (1994), pp. 127-150.
  • [4] P. J. Brockwell and R. A. Davis, Time Series: Theory and Methods, Springer, New York 1987.
  • [5] E. G. Gladyshev, Periodically correlated random sequences, Soviet Math. 2 (1961), pp. 385-388.
  • [6] H. L. Hurd, Almost periodically unitary stochastic processes, Stochastic Process. Appl. 43 (1992), pp. 94-113.
  • [7] H. L. Hurd, A. Makagon and A. G. Miamee, On AR(1) models with periodic and almost periodic coefficients, Stochastic Process. Appl. 100 (2002), pp. 167-185.
  • [8] R. Lund and I. Basawa, Recursive prediction and likelihood evaluation for periodic ARMA models, J. Time Ser. Anal. 21 (2000), pp. 75-93.
  • [9] A. Makagon, Induced stationary process and structure on locally square integrable periodically correlated processes, Studia Math. 136 (1999), pp. 71-86.
  • [10] A. Makagon, A. G. Miamee and H. Salehi, Continuous time periodically correlated processes: Spectrum and prediction, Stochastic Process. Appl. 49 (1994), pp. 277-295.
  • [11] A. Makagon, A. Weron and A. Wyłomańska, Bounded solutions for ARMA models with varying coefficients, Applicationes Mathematicae 31 (3) (2004), pp. 273-285.
  • [12] A. G. Miamee, Periodically correlated processes and their stationary dilations, SIAM J. Appl. Math. 50 (1990), pp. 1194-1199.
  • [13] A. G. Miamee, Explicit formula for the best linear predictor of periodically correlated sequences, SIAM J. Math. 24 (1993), pp. 703-711.
  • [14] A. G. Miamee and H. Salehi, On the prediction of periodically correlated stochastic processes, in: Multivariate Analysis, V. P. R. Krishnaiah (Ed.), North-Holland, Amsterdam 1980, pp. 167-179.
  • [15] A. V. Veccha, Periodic autoregressive moving average (PARMA) modeling with applications to water resources, Water Resources Bulletin 25 (1985), pp. 721-730.
  • [16] A. Weron and A. Wyłomańska, On ARMA (1, q) models with bounded and periodically correlated solutions, Probab. Math. Statist. 24 (2004), pp. 165-172.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-26f38858-54c9-4c2d-874d-a0261f9b6b02
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