On the frequency domain estimation of the innovation variance of a stationary univariate time series

Abstract

The innovation variance σ 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 σ 2 is biased. One way of reducing the small-sample bias in the periodogram ordinates is by tapering. In this paper an estimator of σ 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.