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)