# arch.unitroot.cointegration.engle_granger¶

arch.unitroot.cointegration.engle_granger(y, x, trend='c', *, lags=None, max_lags=None, method='bic')[source]

Test for cointegration within a set of time series.

Parameters
• y (array_like) – The left-hand-side variable in the cointegrating regression.

• x (array_like) – The right-hand-side variables in the cointegrating regression.

• trend ({"n","c","ct","ctt"}, default "c") –

Trend to include in the cointegrating regression. Trends are:

• ”n”: No deterministic terms

• ”c”: Constant

• ”ct”: Constant and linear trend

• ”ctt”: Constant, linear and quadratic trends

• lags (int, default None) – The number of lagged differences to include in the Augmented Dickey-Fuller test used on the residuals of the

• max_lags (int, default None) – The maximum number of lags to consider when using automatic lag-length in the Augmented Dickey-Fuller regression.

• method ({"aic", "bic", "tstat"}, default "bic") – The method used to select the number of lags included in the Augmented Dickey-Fuller regression.

Returns

Results of the Engle-Granger test.

Return type

EngleGrangerTestResults

arch.unitroot.ADF()

Augmented Dickey-Fuller testing.

arch.unitroot.PhillipsPerron()

Phillips & Perron’s unit root test.

arch.unitroot.cointegration.phillips_ouliaris()

Phillips-Ouliaris tests of cointegration.

Notes

The model estimated is

$Y_t = X_t \beta + D_t \gamma + \epsilon_t$

where $$Z_t = [Y_t,X_t]$$ is being tested for cointegration. $$D_t$$ is a set of deterministic terms that may include a constant, a time trend or a quadratic time trend.

The null hypothesis is that the series are not cointegrated.

The test is implemented as an ADF of the estimated residuals from the cross-sectional regression using a set of critical values that is determined by the number of assumed stochastic trends when the null hypothesis is true.