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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 Lag operator ： ウィキペディア英語版 Lag operator In time series analysis, the lag operator or backshift operator operates on an element of a time series to produce the previous element. For example, given some time series :$X=\; \backslash \backslash ,$ then :$\backslash ,\; L\; X\_t\; =\; X\_$ for all $\backslash ;\; t\; >\; 1\backslash ,$ or equivalently :$\backslash ,\; X\_t\; =\; L\; X\_$ for all $\backslash ;\; t\; \backslash geq\; 1\backslash ,$ where ''L'' is the lag operator. Sometimes the symbol ''B'' for backshift is used instead. Note that the lag operator can be raised to arbitrary integer powers so that :$\backslash ,\; L^\; X\_\; =\; X\_\backslash ,$ and :$\backslash ,\; L^k\; X\_\; =\; X\_.\backslash ,$ ==Lag polynomials== Also polynomials of the lag operator can be used, and this is a common notation for ARMA (autoregressive moving average) models. For example, :$\backslash varepsilon\_t\; =\; X\_t\; -\; \backslash sum\_^p\; \backslash varphi\_i\; X\_\; =\; \backslash left(1\; -\; \backslash sum\_^p\; \backslash varphi\_i\; L^i\backslash right)\; X\_t\backslash ,$ specifies an AR(''p'') model. A polynomial of lag operators is called a lag polynomial so that, for example, the ARMA model can be concisely specified as :$\backslash varphi\; (L)\; X\_t\; =\; \backslash theta\; (L)\; \backslash varepsilon\_t\backslash ,$ where $\backslash varphi\; (L)$ and $\backslash theta\; (L)$ respectively represent the lag polynomials :$\backslash varphi\; (L)\; =\; 1\; -\; \backslash sum\_^p\; \backslash varphi\_i\; L^i\backslash ,$ and :$\backslash theta\; (L)=\; 1\; +\; \backslash sum\_^q\; \backslash theta\_i\; L^i.\backslash ,$ Polynomials of lag operators follow similar rules of multiplication and division as do numbers and polynomials of variables. For example, :$X\_t\; =\; \backslash frac\backslash varepsilon\_t,$ means the same thing as :$\backslash varphi\; (L)\; X\_t\; =\; \backslash theta\; (L)\; \backslash varepsilon\_t\backslash ,\; .$ As with polynomials of variables, a polynomial in the lag operator can be divided by another one using polynomial long division. In general dividing one such polynomial by another, when each has a finite order (highest exponent), results in an infinite-order polynomial. An annihilator operator, denoted $()\_+$, removes the entries of the polynomial with negative power (future values). 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「Lag operator」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.