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EXPERIENCES WITH THE BRILLINGER SPECTRAL ESTIMATOR APPLIED TO SIMULATED IRREGULARLY OBSERVED PROCESSES
Author(s) -
Moore Mike I.,
Visser Andy W.,
Shirtcliffe Tim G. L.
Publication year - 1987
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/j.1467-9892.1987.tb00006.x
Subject(s) - mathematics , estimator , autoregressive model , interpolation (computer graphics) , point process , spectrum (functional analysis) , sampling (signal processing) , process (computing) , spectral density estimation , variance (accounting) , independent and identically distributed random variables , interval (graph theory) , statistics , mathematical analysis , combinatorics , random variable , fourier transform , filter (signal processing) , computer science , animation , physics , computer graphics (images) , accounting , quantum mechanics , business , computer vision , operating system
. 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.