statsmodels.stats.diagnostic.acorr_ljungbox(x, lags=None, boxpierce=False) [source]

Ljung-Box test for no autocorrelation

  • x (array_like, 1d) – data series, regression residuals when used as diagnostic test
  • lags (None, int or array_like) – If lags is an integer then this is taken to be the largest lag that is included, the test result is reported for all smaller lag length. If lags is a list or array, then all lags are included up to the largest lag in the list, however only the tests for the lags in the list are reported. If lags is None, then the default maxlag is ‘min((nobs // 2 - 2), 40)’
  • boxpierce ({False, True}) – If true, then additional to the results of the Ljung-Box test also the Box-Pierce test results are returned
  • lbvalue (float or array) – test statistic
  • pvalue (float or array) – p-value based on chi-square distribution
  • bpvalue ((optionsal), float or array) – test statistic for Box-Pierce test
  • bppvalue ((optional), float or array) – p-value based for Box-Pierce test on chi-square distribution


Ljung-Box and Box-Pierce statistic differ in their scaling of the autocorrelation function. Ljung-Box test is reported to have better small sample properties.

TODO: could be extended to work with more than one series 1d or nd ? axis ? ravel ? needs more testing


Looks correctly sized in Monte Carlo studies. not yet compared to verified values


see example script


Greene Wikipedia

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