Editing Autoregressive model (section)

{{Short description|Representation of a type of random process}}
{{More footnotes|date=March 2011}}
In statistics, econometrics, and signal processing, an '''autoregressive''' ('''AR''') '''model''' is a representation of a type of [[stochastic process|random process]]; as such, it can be used to describe certain time-varying processes in nature, economics, behavior, etc. The autoregressive model specifies that the output variable depends linearly on its own previous values and on a [[stochastic]] term (an imperfectly predictable term); thus the model is in the form of a stochastic difference equation (or recurrence relation) which should not be confused with a [[differential equation]]. Together with the [[Moving-average model|moving-average (MA) model]], it is a special case and key component of the more general [[Autoregressive–moving-average model|autoregressive–moving-average]] (ARMA) and [[autoregressive integrated moving average]] (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.

Unlike the moving-average (MA) model, the autoregressive model is not always stationary, because it may contain a unit root.

[[Large language model]]s are called autoregressive, but they are not a classical autoregressive model in this sense because they are not linear.