coint.test: Cointegration Test In aTSA: Alternative Time Series Analysis

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

 `1` ```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`.

Details

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`.

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.

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.

`adf.test`
 ```1 2 3 4 5 6 7 8``` ```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) ```