Time Series ARMA Model Identification by Estimating Information

摘要

Statisticians, economists, and system engineers are becoming aware that to identify models for time series and dynamic systems, information theoretic ideas can play a valuable (and unifying) role. Models for time series Y(t) can be formulated as hypotheses concerning the information about Y(t) given various bases involving past, current, and future values of Y(.) and related time series X(.). To determine sets of variables that are sufficient to forecast Y(t), and especially to determine an ARMA model for Y(t), an approach is presented which estimates and compares various information increments. The author discusses how to non-parametrically estimate the MA(infinity) representation, and use it to form estimators of the many information numbers that might compare to identify an ARMA model for a univariate time series. (Author)