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PEAK‐INSENSITIVE NON‐PARAMETRIC SPECTRUM ESTIMATION
Author(s) -
Sachs Rainer von
Publication year - 1994
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.1467-9892.1994.tb00203.x
Subject(s) - mathematics , estimator , outlier , series (stratigraphy) , parametric statistics , gaussian , frequency domain , asymptotic distribution , kernel density estimation , consistency (knowledge bases) , parametric model , kernel (algebra) , statistics , mathematical analysis , paleontology , physics , geometry , quantum mechanics , combinatorics , biology
. We study the problem of non‐parametric spectrum estimation of a stationary time series that might contain periodic components. In this case the periodogram ordinates have a significant amplitude at frequencies near the frequencies of the periodic components. These can be regarded as outliers in an asymptotically exponential sample. We develop a non‐parametric estimator for the spectral density that is insensitive to these outliers in the frequency domain. This is done by robustifying the usual kernel estimator (smoothed periodogram) by means of M‐estimation in the frequency domain. We propose to use data‐tapered periodograms, which yield a drastic improvement of the procedure, typically for the contaminated situation. This is both shown theoretically and supported by means of simulation. We show consistency of the resulting estimator in the general case, and asymptotic normality in the special case of a Gaussian time series, whether contamination is present or not. Finally we illustrate the finite sample performance of the estimating procedure by some simulation results and by application to the Canadian lynx trappings data.