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A Class of Non‐Embeddable ARMA Processes

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  • A. E. Brockwell
  • P. J. Brockwell

Abstract

We show that a stationary ARMA(p, q) process {Xn = 0, 1, 2, ...} whose moving‐average polynomial has a root on the unit circle cannot be embedded in any continuous‐time autoregressive moving‐average (ARMA) process {Y}(t), t≥ 0}, i.e. we show that it is impossible to find a continuous‐time ARMA process {Y}(t)} whose autocovariance function at integer lags coincides with that of {Xn}. This provides an answer to the previously unresolved question raised in the papers of Chan and Tong (J. Time Ser. Anal. 8 (1987), 277–81), He and Wang (J. Time Ser. Anal. 10 (1989), 315–23) and Brockwell (J. Time Ser. Anal. 16 (1995), 451–60).

Suggested Citation

  • A. E. Brockwell & P. J. Brockwell, 1999. "A Class of Non‐Embeddable ARMA Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 20(5), pages 483-486, September.
    • Handle: RePEc:bla:jtsera:v:20:y:1999:i:5:p:483-486
    DOI: 10.1111/1467-9892.00151
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    Cited by:

    1. Ke Wan & Alain Kornhauser, 2023. "Market Making and Pricing of Financial Derivatives based on Road Travel Times," Papers 2305.02523, arXiv.org, revised May 2023.

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