aTSA (version 3.1.2)

# coint.test: Cointegration Test

## Description

Performs Engle-Granger(or EG) tests for the null hypothesis that two or more time series, each of which is I(1), are not cointegrated.

## Usage

coint.test(y, X, d = 0, nlag = NULL, output = TRUE)

## Arguments

y
the response
X
the exogenous input variable of a numeric vector or a matrix.
d
difference operator for both y and X. The default is 0.
nlag
the lag order to calculate the test statistics. The default is NULL.
output
a logical value indicating to print the results in R console. The default is TRUE.

## Value

• A matrix for test results with three columns (lag, EG, p.value) and three rows (type1, type2, type3). Each row is the test results (including lag parameter, test statistic and p.value) for each type of linear regression models of residuals $z[t]$. See adf.test for more details of three types of linear models.

## Details

To implement the original EG tests, one first has to fit the linear regression $$y[t] = \mu + B*X[t] + e[t],$$ where $B$ is the coefficient vector and $e[t]$ is an error term. With the fitted model, the residuals are obtained, i.e., $z[t] = y[t] - hat{y}[t]$ and a Augmented Dickey-Fuller test is utilized to examine whether the sequence of residuals $z[t]$ is white noise. The null hypothesis of non-cointegration is equivalent to the null hypothesis that $z[t]$ is white noise. See adf.test for more details of Augmented Dickey-Fuller test, as well as the default nlag.

## References

MacKinnon, J. G. (1991). Critical values for cointegration tests, Ch. 13 in Long-run Economic Relationships: Readings in Cointegration, eds. R. F. Engle and C. W. J. Granger, Oxford, Oxford University Press.

adf.test
X <- matrix(rnorm(200),100,2)
coint.test(y,X,d = 1)