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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Autoregressive model ： ウィキペディア英語版 Autoregressive model 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 $AR(p)$ indicates an autoregressive model of order ''p''. The AR(''p'') model is defined as :$X\_t\; =\; c\; +\; \backslash sum\_^p\; \backslash varphi\_i\; X\_+\; \backslash varepsilon\_t\; \backslash ,$ where $\backslash varphi\_1,\; \backslash ldots,\; \backslash varphi\_p$ are the ''parameters'' of the model, $c$ is a constant, and $\backslash varepsilon\_t$ is white noise. This can be equivalently written using the backshift operator ''B'' as :$X\_t\; =\; c\; +\; \backslash sum\_^p\; \backslash varphi\_i\; B^i\; X\_t\; +\; \backslash varepsilon\_t$ so that, moving the summation term to the left side and using polynomial notation, we have :$\backslash phi\; (B)X\_t=\; c\; +\; \backslash varepsilon\_t\; \backslash ,\; .$ 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 $|\backslash varphi\_1\; |\; \backslash geq\; 1$ are not stationary. More generally, for an AR(''p'') model to be wide-sense stationary, the roots of the polynomial $\backslash textstyle\; z^p\; -\; \backslash sum\_^p\; \backslash varphi\_i\; z^$ must lie within the unit circle, i.e., each root $z\_i$ 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 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.