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Forecasting Of Multivariate Periodic Autoregressive Moving‐Average Processes

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  • Taylan A. Ula

Abstract

. Minimum mean square error forecasting of multivariate autoregressive moving‐average processes with periodically varying parameters and orders is considered. General expressions are obtained for the forecasts, their errors and the covariance matrices of the forecast errors. Recursive evaluations of these quantities are shown to follow from the conditional expectation approach. Prediction ellipsoids and intervals for future values of the process are given. Update equations for the forecasts are obtained. The general results are illustrated and verified for a particular case of the process. A simulated example is given.

Suggested Citation

  • Taylan A. Ula, 1993. "Forecasting Of Multivariate Periodic Autoregressive Moving‐Average Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 14(6), pages 645-657, November.
    • Handle: RePEc:bla:jtsera:v:14:y:1993:i:6:p:645-657
    DOI: 10.1111/j.1467-9892.1993.tb00172.x
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    Cited by:

    1. Paul L. Anderson & Mark M. Meerschaert, 2005. "Parameter Estimation for Periodically Stationary Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 26(4), pages 489-518, July.
    2. Aleksandra Grzesiek & Prashant Giri & S. Sundar & Agnieszka WyŁomańska, 2020. "Measures of Cross‐Dependence for Bidimensional Periodic AR(1) Model with α‐Stable Distribution," Journal of Time Series Analysis, Wiley Blackwell, vol. 41(6), pages 785-807, November.
    3. Paul L. Anderson & Farzad Sabzikar & Mark M. Meerschaert, 2021. "Parsimonious time series modeling for high frequency climate data," Journal of Time Series Analysis, Wiley Blackwell, vol. 42(4), pages 442-470, July.
    4. Daniel Dzikowski & Carsten Jentsch, 2024. "Structural Periodic Vector Autoregressions," Papers 2401.14545, arXiv.org.

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