Time series analysis in a frequency subband

Abstract

Standard time series analysis estimates the power spectral density over the full frequency range, until half the sampling frequency. In several input-output identification problems, frequency selective model estimation is desirable. Processing of a time series in a subband may also be useful if observations of a stochastic process are analyzed for the presence or multiplicity of spectral peaks. If two close spectral peaks are present, a minimum number of observations is required to observe two separate narrow peaks with sufficient statistical reliability. Otherwise, with less data, a model with one single broad peak might be selected. A high order autoregressive model will always indicate the separate peaks in the power spectral density, together with many other similar details that are not significant. However, order selection among full-range models may select a model with a single peak. By using subband order selection, 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 subband analysis.