Multitaper estimation of the innovation variance of a stationary time series

Accurate computation of the innovation variance of a stationary time series by a nonparametric method provides useful information to judge the quality of fit of parametric models for the time series. Previous estimators of the innovation variance have made use of raw periodogram ordinates, smoothed periodogram ordinates, or periodogram ordinates following tapering. Smoothing provides more degrees of freedom at each frequency but fewer independent estimates, whereas tapering reduces side-lobe leakage if the dynamic range of the spectrum is high but produces only two degrees of freedom at each frequency. Here, we investigate estimation of innovation variance from finite sample sizes by the use of multiple tapering. The tapers are designed to reduce side-lobe leakage and produce increased degrees of freedom at each frequency. It is demonstrated that the multiple tapering approach produces much better estimates of the innovations variance than the other methods when the spectrum has a high dynamic range and/or is rapidly varying. The multitaper bandwidth parameter W may be selected using an obvious heuristic approach or by an automatic method. The multitaper method is hence an attractive alternative to conventional techniques