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Parameter Estimation For Periodic Arma Models

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  • G. J. Adams
  • G. C. Goodwin

Abstract

. In time series analysis of data sequences, the estimation of the parameters of an identified autoregressive moving‐average (ARMA) model is a well‐known and straightforward exercise. However, if the parameters of the model are periodic (i.e. a periodic ARMA (PARMA) model) then the estimation process becomes more difficult. This paper describes an on‐line parameter estimation technique, based on methods from automatic control, which is demonstrated to provide consistent estimates of PARMA model parameters.

Suggested Citation

  • G. J. Adams & G. C. Goodwin, 1995. "Parameter Estimation For Periodic Arma Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 16(2), pages 127-145, March.
    • Handle: RePEc:bla:jtsera:v:16:y:1995:i:2:p:127-145
    DOI: 10.1111/j.1467-9892.1995.tb00226.x
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    References listed on IDEAS

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    1. P. L. Anderson & A. V. Vecchia, 1993. "Asymptotic Results For Periodic Autoregressive Moving‐Average Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 14(1), pages 1-18, January.
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    Cited by:

    1. Bentarzi, Mohamed, 1998. "Model-Building Problem of Periodically Correlatedm-Variate Moving Average Processes," Journal of Multivariate Analysis, Elsevier, vol. 66(1), pages 1-21, 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. Abdelouahab Bibi & Christian Francq, 2003. "Consistent and asymptotically normal estimators for cyclically time-dependent linear models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 55(1), pages 41-68, March.
    4. Hurd, H. & Makagon, A. & Miamee, A. G., 0. "On AR(1) models with periodic and almost periodic coefficients," Stochastic Processes and their Applications, Elsevier, vol. 100(1-2), pages 167-185, July.
    5. Anderson, Paul L. & Meerschaert, Mark M. & Vecchia, Aldo V., 1999. "Innovations algorithm for periodically stationary time series," Stochastic Processes and their Applications, Elsevier, vol. 83(1), pages 149-169, September.
    6. Anderson, Paul L. & Kavalieris, Laimonis & Meerschaert, Mark M., 2008. "Innovations algorithm asymptotics for periodically stationary time series with heavy tails," Journal of Multivariate Analysis, Elsevier, vol. 99(1), pages 94-116, January.

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