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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 autocovariance ： ウィキペディア英語版 autocovariance In probability and statistics, given a stochastic process $X=(X\_t)$, the autocovariance is a function that gives the covariance of the process with itself at pairs of time points. With the usual notation ''E''  for the expectation operator, if the process has the mean function $\backslash mu\_t\; =\; E()$, then the autocovariance is given by :$C\_(t,s)\; =\; cov(X\_t,\; X\_s)\; =\; E(-\; \backslash mu\_t)(X\_s\; -\; \backslash mu\_s))\; =\; E(X\_s)\; -\; \backslash mu\_t\; \backslash mu\_s.\backslash ,$ Autocovariance is related to the more commonly used autocorrelation of the process in question. In the case of a random vector $X=(X\_1,\; X\_2,\; ...\; ,\; X\_n)$, the ''autocovariance'' would be a square ''n'' by ''n'' matrix $C\_$ with entries $C\_(j,k)\; =\; cov(X\_j,\; X\_k).\backslash ,$ This is commonly known as the covariance matrix or matrix of covariances of the given random vector. == Stationarity == If ''X''(''t'') is stationary process, then the following are true: :$\backslash mu\_t\; =\; \backslash mu\_s\; =\; \backslash mu\; \backslash ,$ for all ''t'', ''s'' and :$C\_(t,s)\; =\; C\_(s-t)\; =\; C\_(\backslash tau)\backslash ,$ where :$\backslash tau\; =\; |s\; -\; t\; |\; \backslash ,$ is the lag time, or the amount of time by which the signal has been shifted. As a result, the autocovariance becomes :$C\_(\backslash tau)\; =\; E(-\; \backslash mu)(X(t+\backslash tau)\; -\; \backslash mu))\backslash ,$ ::::$=\; E(X(t+\backslash tau))\; -\; \backslash mu^2\backslash ,$ ::::$=\; \backslash sigma^2\; R\_(\backslash tau)\; -\; \backslash mu^2,\backslash ,$ where $R\_(\backslash tau)$ is the autocorrelation of the signal with variance $\backslash sigma^2$. Some authors do not normalize the autocorrelation function.〔http://ece-research.unm.edu/bsanthan/ece541/stat.pdf〕 In those literatures, $C\_(\backslash tau)=\; R\_(\backslash tau)\; -\; \backslash mu^2,\backslash ,$. 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「autocovariance」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.