coint.test {aTSA} | R Documentation |
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 |
nlag |
the lag order to calculate the test statistics. The default is |
output |
a logical value indicating to print the results in R console.
The default is |
Details
To implement the original EG tests, one first has to fit the linear regression
where is the coefficient vector and
is an error term.
With the fitted model, the residuals are obtained, i.e.,
and a Augmented Dickey-Fuller test is utilized to examine whether the sequence of
residuals
is white noise. The null hypothesis of non-cointegration
is equivalent to the null hypothesis that
is white noise. See
adf.test
for more details of Augmented Dickey-Fuller test, as well as the default nlag
.
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
. See
adf.test
for more details of three types of linear models.
Author(s)
Debin Qiu
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.
See Also
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)