# egcitest

Engle-Granger cointegration test

## Syntax

## Description

returns
the rejection decision `h`

= egcitest(`Y`

)`h`

from conducting the Engle-Granger
cointegration test for assessing the null hypothesis of no cointegration among the variables
in the multivariate time series `Y`

. `egcitest`

forms test statistics by regressing the response data `Y(:,1)`

onto the
predictor data `Y(:,2:end)`

, and then tests the residuals for a unit
root.

returns the table `StatTbl`

= egcitest(`Tbl`

)`StatTbl`

containing variables for the test results,
statistics, and settings from conducting the Engle-Granger cointegration test on the
variables of the table or timetable `Tbl`

.

The response variable in the regression is the first table variable, and all other
variables are the predictor variables. To select a different response variable for the
regression, use the `ResponseVariable`

name-value argument. To select
different predictor variables, use the `PredictorNames`

name-value
argument.

`[___] = egcitest(___,`

specifies options using one or more name-value arguments in
addition to any of the input argument combinations in previous syntaxes.
`Name=Value`

)`egcitest`

returns the output argument combination for the
corresponding input arguments.

Some options control the number of tests to conduct. The following conditions apply when
`egcitest`

conducts multiple tests:

For example, ```
egcitest(Tbl,ResponseVariable="GDP",Alpha=0.025,Lags=[0
1])
```

chooses `GDP`

as the response variable from the table
`Tbl`

and conducts two tests at a level of significance of 0.025. The
first test includes `0`

lag in the residual regression, and the second test
includes `1`

lag in the residual regression.

`[___,`

additionally returns the following structures of regression statistics, which are required
to form the test statistic:`reg1`

,`reg2`

] = egcitest(___)

`reg1`

– Statistics resulting from the cointegrating regression of the specified response variable`ResponseVariable`

onto the specified predictor variables`PredictorVariables`

`reg2`

– Statistics resulting from the residual regression implemented by the specified unit root test`RReg`

## Examples

## Input Arguments

## Output Arguments

## Tips

To draw valid inferences from the test, determine a suitable value for

`Lags`

. For more details, see the`adftest`

Tips and the`pptest`

Tips.Samples with less than approximately 20 through 40 observations (depending on the dimension of the data

`numDims`

) can yield unreliable critical values, and therefore unreliable inferences. See [3].If a test result suggests that the time series are cointegrated, you can use the residuals as data for the error-correction term in a VEC representation of the variables. Follow this procedure:

## Alternative Functionality

### App

The **Econometric Modeler** app
enables you to conduct the Engle-Granger cointegration test.

## References

[2] Hamilton, James D. *Time Series Analysis*. Princeton, NJ: Princeton University Press, 1994.

## Version History

**Introduced in R2011a**