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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 Ljung–Box test ： ウィキペディア英語版 Ljung–Box test The Ljung–Box test (named for Greta M. Ljung and George E. P. Box) is a type of statistical test of whether any of a group of autocorrelations of a time series are different from zero. Instead of testing randomness at each distinct lag, it tests the "overall" randomness based on a number of lags, and is therefore a portmanteau test. This test is sometimes known as the Ljung–Box Q test, and it is closely connected to the Box–Pierce test (which is named after George E. P. Box and David A. Pierce). In fact, the Ljung–Box test statistic was described explicitly in the paper that led to the use of the Box-Pierce statistic,〔〔 and from which that statistic takes its name. The Box-Pierce test statistic is a simplified version of the Ljung–Box statistic for which subsequent simulation studies have shown poor performance. The Ljung–Box test is widely applied in econometrics and other applications of time series analysis. ==Formal definition== The Ljung–Box test can be defined as follows. : H0: The data are independently distributed (i.e. the correlations in the population from which the sample is taken are 0, so that any observed correlations in the data result from randomness of the sampling process). : Ha: The data are not independently distributed; they exhibit serial correlation. The test statistic is:〔 :$$ Q = n\left(n+2\right)\sum_^h\frac where ''n'' is the sample size, $\backslash hat\_k$ is the sample autocorrelation at lag ''k'', and ''h'' is the number of lags being tested. Under $H\_0$ the statistic Q follows a $\backslash chi^2\_$. For significance level α, the critical region for rejection of the hypothesis of randomness is : $$ Q > \chi_^2 where $\backslash chi\_^2$ is the α-quantile of the chi-squared distribution with ''h'' degrees of freedom. The Ljung–Box test is commonly used in autoregressive integrated moving average (ARIMA) modeling. Note that it is applied to the residuals of a fitted ARIMA model, not the original series, and in such applications the hypothesis actually being tested is that the residuals from the ARIMA model have no autocorrelation. When testing the residuals of an estimated ARIMA model, the degrees of freedom need to be adjusted to reflect the parameter estimation. For example, for an ARIMA(p,0,q) model, the degrees of freedom should be set to $h\; -\; p\; -\; q$. 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「Ljung–Box test」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.