论文信息 - MAXIMUM LIKELIHOOD ESTIMATION FOR PERIODIC AUTOREGRESSIVE MOVING AVERAGE MODELS.

MAXIMUM LIKELIHOOD ESTIMATION FOR PERIODIC AUTOREGRESSIVE MOVING AVERAGE MODELS.

A useful class of models for seasonal time series that cannot be filtered or standardized to achieve second-order stationarity is that of periodic autoregressive moving average (PARMA) models, which are extensions of ARMA models that allow periodic (seasonal) parameters. An approximation to the exact likelihood for Gaussian PARMA processes is developed, and a straightforward algorithm for its maximization is presented. The algorithm is tested on several periodic ARMA(l, 1) models through simulation studies and is compared to moment estimation via the seasonal Yule–Walker equations. Applicability of the technique is demonstrated through an analysis of a seasonal stream-flow series from the Rio Caroni River in Venezuela.

A. V. Vecchia

[1] Jose D. Salas,et al. Estimation of ARMA Models with seasonal parameters , 1982 .

[2] Marcello Pagano,et al. On Periodic and Multiple Autoregressions , 1978 .

[3] R H Jones,et al. Time series with periodic structure. , 1967, Biometrika.

[4] George E. P. Box,et al. Time Series Analysis: Forecasting and Control , 1977 .

[5] Steven C. Hillmer,et al. Likelihood Function of Stationary Multiple Autoregressive Moving Average Models , 1979 .

[6] G. C. Tiao,et al. Hidden Periodic Autoregressive-Moving Average Models in Time Series Data, , 1980 .

[7] Gwilym M. Jenkins,et al. Time series analysis, forecasting and control , 1972 .

[8] D. B. Preston. Spectral Analysis and Time Series , 1983 .

[9] B. Troutman. Some results in periodic autoregression , 1979 .