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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 Moving-average model ： ウィキペディア英語版 Moving-average model In time series analysis, the moving-average (MA) model is a common approach for modeling univariate time series. The notation MA(''q'') refers to the moving average model of order ''q'': :$X\_t\; =\; \backslash mu\; +\; \backslash varepsilon\_t\; +\; \backslash theta\_1\; \backslash varepsilon\_\; +\; \backslash cdots\; +\; \backslash theta\_q\; \backslash varepsilon\_\; \backslash ,$ where μ is the mean of the series, the ''θ''1, ..., ''θ''''q'' are the parameters of the model and the ''ε''''t'', ''ε''''t''−1,..., ''ε''''t''−q are white noise error terms. The value of ''q'' is called the order of the MA model. This can be equivalently written in terms of the backshift operator ''B'' as :$X\_t\; =\; \backslash mu\; +\; (1\; +\; \backslash theta\_1\; B\; +\; \backslash cdots\; +\; \backslash theta\_q\; B^q)\backslash varepsilon\_t.$ Thus, a moving-average model is conceptually a linear regression of the current value of the series against current and previous (unobserved) white noise error terms or random shocks. The random shocks at each point are assumed to be mutually independent and to come from the same distribution, typically a normal distribution, with location at zero and constant scale. ==Interpretation== The moving-average model is essentially a finite impulse response filter applied to white noise, with some additional interpretation placed on it. The role of the random shocks in the MA model differs from their role in the autoregressive (AR) model in two ways. First, they are propagated to future values of the time series directly: for example, $\backslash varepsilon\; \_$ appears directly on the right side of the equation for $X\_t$. In contrast, in an AR model $\backslash varepsilon\; \_$ does not appear on the right side of the $X\_t$ equation, but it does appear on the right side of the $X\_$ equation, and $X\_$ appears on the right side of the $X\_t$ equation, giving only an indirect effect of $\backslash varepsilon\_$ on $X\_t$. Second, in the MA model a shock affects $X$ values only for the current period and ''q'' periods into the future; in contrast, in the AR model a shock affects $X$ values infinitely far into the future, because $\backslash varepsilon\; \_t$ affects $X\_t$, which affects $X\_$, which affects $X\_$, and so on forever. 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「Moving-average 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.