Multirate autoregressive modeling

In many practical situations, an experimenter is interested in the behavior of a process at different time scales T. In this paper it is shown that autoregressive (AR) parameter estimation and order selection can be reformulated to find the best model for the signal properties at interval T. A comparison between AR modeling at interval T and standard AR modeling shows that modeling at interval T can be more accurate in the reduced frequency interval as a result of better order selection. More accurate results can be expected when the model order selected with standard AR analysis is lower than the true order. This occurs when the true process is an AR process with a number of insignificant trailing parameters, or when the true process is AR(∞), e.g. due to additive noise in the data.