References
- Adams , G. J. , Goodwin , G. C. ( 1995 ). Parameter estimation for periodic ARMA models . Journal of Time Series Analysis 16 : 127 – 145 .
- Akaike , H. ( 1974 ). A new look at the statistical model identification . IEEE Transactions on Automatic Control AC-19 : 716 – 723 .
- Anderson , P. L. , Vecchia , A. V. ( 1993 ). Asymptotic results for periodic autoregressive moving-average processes . Journal of Time Series Analysis 14 : 1 – 18 .
- Bai , Z. D. , Subramanyam , Zhao , K., L. C. ( 1988 ). On determination of the order of an autoregressive model . Journal of Multivariate Analysis 27 : 40 – 52 .
- Bentarzi , M. ( 1998 ). Model-building problem of periodicallys m-variete moving average process . Journal of Multivariate Analysis 66 : 1 – 21 .
- Bentarzi , M. , Hallin , M. ( 1994 ). On the invertibility of periodic moving average models . Journal of Time Series Analysis 15 : 263 – 268 .
- Bentarzi , M. , Aknouche , A. ( 2005 ). Calculation of the Fisher information matrix for periodic ARMA models . Communications in Statistics Theory and Methods 34 : 891 – 903 .
- Boshnakov , G. N. ( 1996 ). Recursive computation of the parameters of periodic autoregressive moving-average processes . Journal of Time Series Analysis 17 : 333 – 349 .
- Box , G. E. P. , Jenkins , G. M. ( 1976 ). Time Series Analysis, Forecasting and Control. , Rev. ed. San Francisco : Holden-Day .
- Box , G. E. P. , Tiao , G. C. ( 1992 ). Bayesian Inference in Statistical Analysis . Wiley-Interscience .
- Ciftcioglu , Ö. , Hoogenboom , J. E. , Dam , H. V. (1994). A consistent estimator for the model order of an autoregressive process. IEEE Transactions on Signal Processing 42:1471–1476.
- Djuric' , P. M. , Kay , S. M. ( 1992 ). Order selection of autoregressive models . IEEE Transactions on Signal Processing 40 : 2829 – 2833 .
- Franses , P. H. ( 1996 ). Periodicity and Stochastic Trends in Economic Time Series . Oxford : Oxford University Press .
- Herwartz , H. ( 1997 ). Performance of periodic error correction models in forecasting consumption data . International Journal of Forecasting 13 : 421 – 431 .
- Osborn , D. R. ( 1991 ). The implications of periodically varying coefficients for seasonal time series processes . Journal of Econometrics 48 : 373 – 384 .
- Osborn , D. R. , Smith , J. P. ( 1989 ). The performance of periodic autoregressive models in forecasting seasonal U.K. consumption . Journal of Business and Economic Statistics 7 : 117 – 127 .
- Pagano , M. ( 1978 ). On periodic and multiple autoregression . Annals of Statistics 6 : 1310 – 1317 .
- Rissanen , J. ( 1978 ). Modeling by shortest data description . Automatica 14 : 465 – 478 .
- Schwarz , G. ( 1978 ). Estimating the dimension of the model . Annals of Statistics 6 : 461 – 664 .
- Shibata , R. ( 1976 ). Selection of the order of an autoregressive model by Akaike's information criterion . Biometrika 63 : 117 – 126 .
- Ula , T. A. ( 1990 ). Periodic covariance stationarity of multivariate periodic autoregressive moving average processes . Water Resource Research 26 : 855 – 861 .
- Ula , T. A. ( 1993 ). Forecasting of multivariate periodic autoregressive moving average processes . Journal of Time Series Analysis 14 : 645 – 657 .
- Ula , T. A. , Smadi , A. A. ( 1997 ). Periodic stationary conditions for periodic autoregressive moving average processes as eigenvalues problems . Water Resource Research 33 : 1929 – 1934 .
- Vecchia , A. V. ( 1985 ). Periodic autoregressive-moving average (PARMA) modeling with application to water resources . Water Resource Bulletin 21 : 721 – 730 .
- Vecchia , A. V. , Ballerini , R. ( 1992 ). Testing for periodic autocorrelations in seasonal time series data . Biometrika 78 : 53 – 63 .