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Biometrika 1985 72(2):317-323; doi:10.1093/biomet/72.2.317
© 1985 by Biometrika Trust
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On the frequency domain estimation of the innovation variance of a stationary univariate time series

TARMO PUKKILA and HANS NYQUIST

Department of Mathematical Sciences, University of Tampere Tampere, SF-33101, Finland
Department of Statistics, University of Umeå Umeå, S-901 87, Sweden

The innovation variance {sigma}2 of a linear stochastic time series model can be estimated using periodogram ordinates. However, since the periodogram ordinates as estimators of the corresponding spectrum ordinates can show appreciable small-sample bias, it is believed that the estimator of {sigma}2 is biased. One way of reducing the small-sample bias in the periodogram ordinates is by tapering. In this paper an estimator of {sigma}2 based on tapered time series is defined and evaluated analytically as well as by simulation. Tapering has a large bias-reducing as well as variance-reducing effect when the roots of the characteristic equation of the model are close to the unit circle.

Key Words: Bias • Innovation variance • Periodogram • Stationary time series • Tapering


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