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Peak‐Insensitive Non‐Parametric Spectrum Estimation

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  • Rainer von Sachs

Abstract

. 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.

Suggested Citation

  • Rainer von Sachs, 1994. "Peak‐Insensitive Non‐Parametric Spectrum Estimation," Journal of Time Series Analysis, Wiley Blackwell, vol. 15(4), pages 429-452, July.
    • Handle: RePEc:bla:jtsera:v:15:y:1994:i:4:p:429-452
    DOI: 10.1111/j.1467-9892.1994.tb00203.x
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    Cited by:

    1. von Sachs, Rainer, 2019. "Spectral Analysis of Multivariate Time Series," LIDAM Discussion Papers ISBA 2019008, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).

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