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

Ljung-Box test for no autocorrelation

xarray_like, 1d

data series, regression residuals when used as diagnostic test

lagsNone, 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

lbvaluefloat or array

test statistic

pvaluefloat or array

p-value based on chi-square distribution

bpvalue(optional), 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


Greene Wikipedia


see example script