Autoregression
In statistics and signal processing, an autoregressive (AR) model is a representation of a type of random process; as such, it is used to describe certain time-varying processes in nature, economics, etc. The autoregressive model specifies that the output variable depends linearly on its own previous values and on a term (an imperfectly predictable term); thus the model is in the form of a stochastic difference equation.
Together with the moving-average (MA) model, it is a special case and key component of the more general ARMA and ARIMA models of time series, which have a more complicated stochastic structure; it is also a special case of the vector autoregressive model (VAR), which consists of a system of more than one interlocking stochastic difference equation in more than one evolving random variable.
Contrary to the moving-average model, the autoregressive model is not always stationary as it may contain a unit root.
The notation indicates an autoregressive model of order p. The AR(p) model is defined as
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