The direct connection between box & Jenkins methodology and adaptive filtering theory

Abstract

This work discusses the direct relation between linear tools to solve forecasting tasks: Autoregressive (AR) and Autoregressive and Moving Average (ARMA) models, from Box \& Jenkins methodology, and the Finite and Impulse response linear adaptive filters. The aforementioned filters are commonly used in channel equalization, but they also can be used to perform predictions. It is presented the similarities, differences and the distinct concepts of transfer function. We show their structures and a comparative overview, as the time series forecasting field and the Adaptive Filter Theory do not present the details of the connection between the proposals.