# statsmodels.stats.diagnostic.acorr_lm¶

statsmodels.stats.diagnostic.acorr_lm(resid, nlags=None, autolag='AIC', store=False, *, period=None, ddof=0, cov_type='nonrobust', cov_kwargs=None)[source]

Lagrange Multiplier tests for autocorrelation.

This is a generic Lagrange Multiplier test for autocorrelation. Returns Engle’s ARCH test if resid is the squared residual array. Breusch-Godfrey is a variation on this test with additional exogenous variables.

Parameters
residarray_like

Time series to test.

nlagsint, default None

Highest lag to use. The behavior of this parameter will change after 0.12.

autolag{str, None}, default “AIC”

If None, then a fixed number of lags given by maxlag is used. This parameter is deprecated and will be removed after 0.12. Searching for model specification cannot control test size.

storebool, default False

If true then the intermediate results are also returned.

periodint, default none

The period of a Seasonal time series. Used to compute the max lag for seasonal data which uses min(2*period, nobs // 5) if set. If None, then the default rule is used to set the number of lags. When set, must be >= 2.

ddofint, default 0

The number of degrees of freedom consumed by the model used to produce resid. The default value is 0.

cov_typestr, default “nonrobust”

Covariance type. The default is “nonrobust which uses the classic OLS covariance estimator. Specify one of “HC0”, “HC1”, “HC2”, “HC3” to use White’s covariance estimator. All covariance types supported by OLS.fit are accepted.

cov_kwargsdict, default None

Dictionary of covariance options passed to OLS.fit. See OLS.fit for more details.

Returns
lmfloat

Lagrange multiplier test statistic.

lmpvalfloat

The p-value for Lagrange multiplier test.

fvalfloat

The f statistic of the F test, alternative version of the same test based on F test for the parameter restriction.

fpvalfloat

The pvalue of the F test.

res_storeResultsStore, optional

Intermediate results. Only returned if store=True.

het_arch

Conditional heteroskedasticity testing.

acorr_breusch_godfrey

Breusch-Godfrey test for serial correlation.

acorr_ljung_box`

Ljung-Box test for serial correlation.

Notes

The test statistic is computed as (nobs - ddof) * r2 where r2 is the R-squared from a regression on the residual on nlags lags of the residual.