coint

coint(Y0, Y1, [trend="c"], [method="aeg"], [maxLag], [autoLag="aic"])

Y0 is a numeric vector indicating the first element in cointegrated system. NULL values are not supported.

Y1 is a numeric vector or matrix indicating the remaining elements in cointegrated system. The number of elements in Y1 and Y0 must be equal. NULL values are not supported.

trend is a scalar specifying the trend term included in regression for cointegrating equation. It can be

• "c" : constant.

• "ct" : constant and linear trend.

• "ctt" : constant, and linear and quadratic trend.

• "n" : no constant, no trend.

method is a string indicating the method for cointegration testing. Only "aeg" (augmented Engle-Granger) is available.

maxLag is a non-negative integer indicating the largest number of lags, which is used as an argument for adfuller.

autoLag is a string indicating the lag selection criterion, which is used as an argument for adfuller. It can be:

• "aic": The number of lags is chosen to minimize the Akaike information criterion.

• "bic": The number of lags is chosen to minimize the Bayesian information criterion.

• "tstat": Start with maxLag and drops a lag until the t-statistic on the last lag length is significant using a 5%-sized test.

• "max": The number of included lags is set to maxLag.

Test for no-cointegration of a univariate equation.

Return value: A dictionary containing the following keys

• tStat: A floating-point scalar indicating the t-statistic of unit-root test on residuals.

• pValue: A floating-point scalar indicating the MacKinnon's approximate p-value based on MacKinnon (1994, 2010).

• criticalValues: A dictionary containing the critical values for the test statistic at the 1 %, 5 %, and 10 % levels based on regression curve.

Y0 = 234 267 289 301 312 323 334 345 356;
Y1 = 267 289 301 312 323 334 345 356 367;
coint(Y0, Y1);

A dictionary is returned:

tValue->-1.498236972489574
pValue->0.761867238199341
criticalValues->[-5.789286875000001,-4.206501875,-3.6171]