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Experiences With The Brillinger Spectral Estimator Applied To Simulated Irregularly Observed Processes

Author

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  • Mike I. Moore
  • Andy W. Visser
  • Tim G. L. Shirtcliffe

Abstract

. Shannon interpolation is used to assign values from a readily simulated discrete time process to the times of a point process, simulated by Ogata's thinning technique. The result is a set of unequally spaced samples from a hypothetical continuous time process with spectrum equal to that of the discrete time process for frequencies |ω| ≤π/Δ and identically equal to zero for |ω| > π/Δ, where Δ is the discrete time step. The spectra are theoretically known both for the sampled process and for the sampling point process. We calculate Brillinger spectral estimates for examples of a process with autoregressive spectrum, sampled at the times of a Hawkes Self Exciting Point Process. The success of the Brillinger estimator is demonstrated but it is shown to have an inherently high variance. An approximate confidence interval is discussed.

Suggested Citation

  • Mike I. Moore & Andy W. Visser & Tim G. L. Shirtcliffe, 1987. "Experiences With The Brillinger Spectral Estimator Applied To Simulated Irregularly Observed Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 8(4), pages 433-442, July.
    • Handle: RePEc:bla:jtsera:v:8:y:1987:i:4:p:433-442
    DOI: 10.1111/j.1467-9892.1987.tb00006.x
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    Cited by:

    1. Peter Thomson & Peter Robinson, 1996. "Estimation of second-order properties from jittered time series," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 48(1), pages 29-48, March.
    2. Keh‐Shin Lii & Tai‐Houn Tsou, 1995. "Bispectral Analysis Of Randomly Sampled Data," Journal of Time Series Analysis, Wiley Blackwell, vol. 16(1), pages 43-66, January.

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