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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 fractionally integrated moving average ： ウィキペディア英語版 Autoregressive fractionally integrated moving average In statistics, autoregressive fractionally integrated moving average models are time series models that generalize ARIMA (''autoregressive integrated moving average'') models by allowing non-integer values of the differencing parameter. These models are useful in modeling time series with long memory—that is, in which deviations from the long-run mean decay more slowly than an exponential decay. The acronyms "ARFIMA" or "FARIMA" are often used, although it is also conventional to simply extend the "ARIMA(''p'',''d'',''q'')" notation for models, by simply allowing the order of differencing, ''d'', to take fractional values. ==Basics== In an ARIMA model, the ''integrated'' part of the model includes the differencing operator (1 − ''B'') (where ''B'' is the backshift operator) raised to an integer power. For example :$(1-B)^2=1-2B+B^2\; \backslash ,,$ where :$B^2X\_t=X\_\; \backslash ,\; ,$ so that :$(1-B)^2X\_t\; =\; X\_t\; -2X\_\; +\; X\_.$ In a ''fractional'' model, the power is allowed to be fractional, with the meaning of the term identified using the following formal binomial series expansion :$\backslash begin$ (1 - B)^d &= \sum_^ \; \; (-B)^k \\ & = \sum_^ \; \frac (d - a)\ (-B)^k}\\ &=1-dB+\fracB^2 -\cdots \, . \end 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 fractionally integrated moving average」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.