coint.test {aTSA} | R Documentation |
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.
coint.test(y, X, d = 0, nlag = NULL, output = TRUE)
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 |
To implement the original EG tests, one first has to fit the linear regression
y[t] = μ + 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
.
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.
Debin Qiu
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.
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)