Estimation of coherence via ARMA modelling

The magnitude squared coherence (MSC) between two time series is a quantity that measures the degree of similarities between two time series. It is given by the magnitude squared of the cross-spectrum of the two series, normalized by their respective auto-spectra. Existing methods of MSC estimation are Fourier Transform based, using periodograms to find the required spectra. This paper presents a new method of MSC estimation. The pertinent spectral ratios are modelled by auto-regressive-moving average (ARMA) filters whose coefficients are computed by a least squares estimator. Acceptable performance of the estimator is confirmed by simulation studies. However, it is also shown in some instances that results can be poor if reasonably correct model orders are not used. Hence there is a need for a method to determine the optimum ARMA orders.