Autoregressive (AR) Models

The autoregressive (AR) models are used in time series analysis . to describe stationary time series . These models represent time series that are generated by passing the white noise through a recursive linear filter . The output of such a filter at the moment is a weighted sum of previous values of the filter output. The integer parameter is called the order of the AR-model.

The AR-model of a random process in discrete time is defined by the following expression:

 

where

• are the coefficients of the recursive filter;

• is the order of the model;

• are output uncorrelated errors.