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In statistics and signal processing, an autoregressive (AR) model is a representation of a type of random process; as such, it describes 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 stochastic term (a stochastic—an imperfectly predictable—term); thus the model is in the form of a stochastic difference equation. It is a special case of the more general ARMA model of time series, which has 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 stochastic difference equation. ==Definition== The notation indicates an autoregressive model of order ''p''. The AR(''p'') model is defined as : where are the ''parameters'' of the model, is a constant, and is white noise. This can be equivalently written using the backshift operator ''B'' as : so that, moving the summation term to the left side and using polynomial notation, we have : An autoregressive model can thus be viewed as the output of an all-pole infinite impulse response filter whose input is white noise. Some parameter constraints are necessary for the model to remain wide-sense stationary. For example, processes in the AR(1) model with are not stationary. More generally, for an AR(''p'') model to be wide-sense stationary, the roots of the polynomial must lie within the unit circle, i.e., each root must satisfy . 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Autoregressive model」の詳細全文を読む スポンサード リンク
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