Frequency selective time series analysis

Standard time series analysis estimates a full range power spectral density that extends from minus one half to plus one half of the sampling frequency. In several input-output identification problems, frequency selective model estimation is desirable. Selective processing of a time series may also be useful if a number of observations of a stochastic process is analyzed for the presence of spectral peaks. If two close spectral peaks are present, a minimum number of observations is required to observe with sufficient statistical reliability the difference between one single broad peak and two separate narrow peaks. In certain cases a high order autoregressive model describes the separate peaks, together with many other details which are not significant. However, after full range order selection a lower order model with a single peak may be selected with the standard analysis. By using order selection in a smaller subband of the frequency range it is sometimes possible to detect the presence of two peaks from the same data. Therefore, spectral details can be analyzed from fewer observations with a frequency selective analysis.