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:

resid : array_like

Time series to test.

nlags : int, 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.

store : bool, default False

If true then the intermediate results are also returned.

period : int, 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.

ddof : int, default 0

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

cov_type : str, 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_kwargs : dict, default None

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

Returns:

lm : float

Lagrange multiplier test statistic.

lmpval : float

The p-value for Lagrange multiplier test.

fval : float

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

fpval : float

The pvalue of the F test.

res_store : ResultsStore, optional

Intermediate results. Only returned if store=True.

See also

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.