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:
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where
-
are the coefficients of the recursive filter;
-
is the order of the model;
-
are output uncorrelated errors.