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.
[3] The Ljung–Box test is widely applied in econometrics and other applications of time series analysis.
For significance level α, the critical region for rejection of the hypothesis of randomness is: where
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.
For example, for an ARIMA(p,0,q) model, the degrees of freedom should be set to
Simulation studies have shown that the distribution for the Ljung–Box statistic is closer to a
[citation needed] This article incorporates public domain material from the National Institute of Standards and Technology