Multiple time series usually arise in measurements on physical systems in one of two ways. The first way is when a set of time series arise on an 'equal footing.' A distant explosion might be recorded at several contiguous recording sites. From such series can be determined, for example, characteristics of the signal and noise content of the data. The second way is when the series are causally related. Northward and eastward wind velocity series at a coastal location might be inputs to a linear system, which with additive noise produces on output the northward wind velocity at a buoy location. Here we might wish to estimate some properties of the linear system.
Many physical systems exhibit a large dynamic range. We show how the technique of multitaper spectral analysis can be used to much improve the analysis of series which arise on an 'equal footing.' This is illustrated using multiple time series recordings of seismic explosions. We show how multitaper spectral analysis (a) can better detect the presence or absence of 60Hz 'power-line pick-up' for dynamite data recorded in Canada, and (b) more accurately characterize seismic exploration data in terms of coherence and signal-to-noise ratios.
For the case of two causally related time series with additive non-white noise we show how it is possible to calculate a confidence interval for the mean square error of the signal component. This is an advance on traditional methods which merely detect the presence or absence of the signal. The approach is demonstrated using some seismic data recorded at sea.