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A Note On Embedding A Discrete Parameter Arma Model In A Continuous Parameter Arma Model

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  • K. S. Chan
  • H. Tong

Abstract

. We have shown that it is not always possible to embed a real‐valued discrete parameter Gaussian AR(1) model in a real‐valued continuous parameter Gaussian AR(1). The problem with general ARMA models is also discussed.

Suggested Citation

  • K. S. Chan & H. Tong, 1987. "A Note On Embedding A Discrete Parameter Arma Model In A Continuous Parameter Arma Model," Journal of Time Series Analysis, Wiley Blackwell, vol. 8(3), pages 277-281, May.
    • Handle: RePEc:bla:jtsera:v:8:y:1987:i:3:p:277-281
    DOI: 10.1111/j.1467-9892.1987.tb00439.x
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    Cited by:

    1. Valerie Girardin & Rachid Senoussi, 2020. "Filling the gap between Continuous and Discrete Time Dynamics of Autoregressive Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 41(4), pages 590-602, July.
    2. Michael D. Hunter & Haya Fatimah & Marina A. Bornovalova, 2022. "Two Filtering Methods of Forecasting Linear and Nonlinear Dynamics of Intensive Longitudinal Data," Psychometrika, Springer;The Psychometric Society, vol. 87(2), pages 477-505, June.
    3. Peter J. Brockwell, 1995. "A Note On The Embedding Of Discrete‐Time Arma Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 16(5), pages 451-460, September.
    4. Ma, Chunsheng, 2005. "A class of stationary random fields with a simple correlation structure," Journal of Multivariate Analysis, Elsevier, vol. 94(2), pages 313-327, June.
    5. Dette, Holger & Pepelyshev, Andrey & Zhigljavsky, Anatoly, 2016. "Optimal designs for regression models with autoregressive errors," Statistics & Probability Letters, Elsevier, vol. 116(C), pages 107-115.
    6. Tómasson, Helgi, 2011. "Some Computational Aspects of Gaussian CARMA Modelling," Economics Series 274, Institute for Advanced Studies.
    7. Ngai Chan & Yury Kutoyants, 2012. "On parameter estimation of threshold autoregressive models," Statistical Inference for Stochastic Processes, Springer, vol. 15(1), pages 81-104, April.
    8. M. Kessler & A. Rahbek, 2004. "Identification and Inference for Multivariate Cointegrated and Ergodic Gaussian Diffusions," Statistical Inference for Stochastic Processes, Springer, vol. 7(2), pages 137-151, May.
    9. Peter Brockwell & Jens-Peter Kreiss & Tobias Niebuhr, 2014. "Bootstrapping continuous-time autoregressive processes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(1), pages 75-92, February.

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