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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. Tómasson, Helgi, 2011. "Some Computational Aspects of Gaussian CARMA Modelling," Economics Series 274, Institute for Advanced Studies.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    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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