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 lefthandside variable in the cointegrating regression.
x (array_like) – The righthandside 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 DickeyFuller test used on the residuals of the
max_lags (int, default None) – The maximum number of lags to consider when using automatic laglength in the Augmented DickeyFuller regression.
method ({"aic", "bic", "tstat"}, default "bic") – The method used to select the number of lags included in the Augmented DickeyFuller regression.
 Returns
Results of the EngleGranger test.
 Return type
See also
arch.unitroot.ADF()
Augmented DickeyFuller testing.
arch.unitroot.PhillipsPerron()
Phillips & Perron’s unit root test.
arch.unitroot.cointegration.phillips_ouliaris()
PhillipsOuliaris 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 crosssectional regression using a set of critical values that is determined by the number of assumed stochastic trends when the null hypothesis is true.