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
 ynumpy:array_like
The lefthandside variable in the cointegrating regression.
 xnumpy: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
EngleGrangerTestResults
Results of the EngleGranger test.
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.
 Return type
EngleGrangerTestResults