Estimation of partial group delay with applications to small samples
Partial group delay has an interpretation as a parameter that measures the time-lag relationship between two channels of a multiple time series after adjustments have been made for the influence of the remaining channels. The time-lagged relationship is typically studied frequency by frequency. In this dissertation a procedure for estimating the partial group delay parameter is proposed which is intended to work well even for small sample sizes. The only published procedure for estimating the partial group delay parameter is by Zhang and Foutz . The procedure by them is an asymptotic one and requires a fairly large sample size.
The proposed procedure for estimating the partial group delay parameter uses the frequency domain approach of time series analysis. The frequency domain approach is also known as spectral analysis and models a time series using sine-cosine functions. The two most important spectral tools used in the dissertation are the discrete Fourier transform and the periodogram ordinates.
The procedure consists of finding preliminary values for the partial group delay parameter. The mean of the preliminary values is then estimated using transforming and modeling techniques on the preliminary values. A key requirement for the procedure is that the periodogram and cross periodogram ordinates at each Fourier frequency are independent of the periodogram and cross periodogram ordinates at all other Fourier frequencies. Under this requirement, the estimate is uniformly minimum variance unbiased. The key requirement is satisfied as the sample size increases or if the channels of the multiple time series are Gaussian white noise processes and are not cross correlated. The performance of the procedure is demonstrated using a simulation study and is compared to the only published procedure by Zhang and Foutz .