# 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

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.## Examples

X <- matrix(rnorm(200),100,2)
y <- 0.3*X[,1] + 1.2*X[,2] + rnorm(100)
# test for original y and X
coint.test(y,X)
# test for response = diff(y,differences = 1) and
# input = apply(X, diff, differences = 1)
coint.test(y,X,d = 1)