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.