EXPERIENCES WITH THE BRILLINGER SPECTRAL ESTIMATOR APPLIED TO SIMULATED IRREGULARLY OBSERVED PROCESSES

Mike I. Moore, Andy W. Visser and Tim G. L. Shirtcliffe

Journal of Time Series Analysis, 1987, vol. 8, issue 4, 433-442

Abstract: 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.

Date: 1987
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