# jcitest

Johansen cointegration test

## Syntax

## Description

returns
rejection decisions from conducting the Johansen test, which assesses each null hypothesis `h`

= jcitest(`Y`

)*H*(*r*) of cointegration rank less than or equal to *r* among an
input `numDims`

-dimensional multivariate time series against the
alternatives *H*(`numDims`

) (`trace`

test) or *H*(*r* + 1) (`maxeig`

test).
The tests produce maximum likelihood estimates of the parameters in a vector
error-correction (VEC) model of the cointegrated series.

returns
rejection decisions from conducting the Johansen test on the variables of an input table or
timetable.`h`

= jcitest(`Tbl`

)

To select a subset of variables to test, use the `DataVariables`

name-value argument.

uses additional options specified by one or more name-value arguments, using any
input-argument combination in the previous syntaxes.`h`

= jcitest(___,`Name=Value`

)

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

conducts multiple tests:

`jcitest`

treats each test as separate from all other tests.Each row of all outputs contains the results of the corresponding test.

For example, `jcitest(Tbl,Model="H2",DataVariables=1:5)`

tests the
first 5 variables in the input table `Tbl`

using the Johansen model that
excludes all deterministic terms.

`[`

displays, at the command window, the results of the Johansen test and returns the
`h`

,`pValue`

,`stat`

,`cValue`

]
= jcitest(___)*p*-values `pValue`

, test statistics
`stat`

, and critical values `cValue`

of the test.
The results display includes the ranks *r*, corresponding rejection
decisions, *p*-values, decision statistics, and specified options.

## Examples

## Input Arguments

## Output Arguments

## More About

## Tips

## Algorithms

`jcitest`

identifies deterministic terms that are outside of the cointegrating relations,*c*_{1}and*d*_{1}, by projecting constant and linear regression coefficients, respectively, onto the orthogonal complement of*A*.If

`jcitest`

fails to reject the null hypothesis of cointegration rank*r*= 0, the inference is that the error-correction coefficient*C*is zero, and the VEC(*q*) model reduces to a standard VAR(*q*) model in first differences. If`jcitest`

rejects all cointegration ranks*r*less than`numDims`

, the inference is that*C*has full rank, and*y*is stationary in levels._{t}The parameters

*A*and*B*in the reduced-rank VEC(*q*) model are not identifiable, but their product*C*=*A**B*′ is identifiable.`jcitest`

constructs`B`

=`V(:,1:`

using the orthonormal eigenvectors)`r`

`V`

returned by`eig`

, and then renormalizes so that`V'*S11*V = I`

[3].The time series in the specified input data can be stationary in levels or first differences (that is,

*I*(0) or*I*(1)). Rather than pretesting series for unit roots (using, e.g.,`adftest`

,`pptest`

,`kpsstest`

, or`lmctest`

), the Johansen procedure formulates the question within the model. An*I*(0) series is associated with a standard unit vector in the space of cointegrating relations, and the`jcontest`

can test for its presence.*Deterministic cointegration*, where cointegrating relations, perhaps with an intercept, produce stationary series, is the traditional sense of cointegration introduced by Engle and Granger [1] (see`egcitest`

).*Stochastic cointegration*, where cointegrating relations produce trend-stationary series (that is,`d0`

is nonzero), extends the definition of cointegration to accommodate a greater variety of economic series.Unless higher-order trends are present in the data, models with fewer restrictions can produce good in-sample fits, but poor out-of-sample forecasts.

## Alternative Functionality

### App

The Econometric Modeler app enables you to conduct the Johansen cointegration test.

## References

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

[3] Johansen, S. *Likelihood-Based Inference in Cointegrated Vector Autoregressive Models*. Oxford: Oxford University Press, 1995.

[5] Turner, P. M. "Testing for
Cointegration Using the Johansen Approach: Are We Using the Correct Critical Values?"
*Journal of Applied Econometrics*. v. 24, 2009, pp.
825–831.

## Version History

**Introduced in R2011a**

## See Also

### Objects

### Functions

### Topics

- Cointegration and Error Correction Analysis
- Identifying Single Cointegrating Relations
- Compare Approaches to Cointegration Analysis
- Test for Cointegration Using the Johansen Test
- Test Cointegrating Vectors
- Estimate VEC Model Parameters Using jcitest
- Testing Cointegrating Vectors and Adjustment Speeds
- Specifying Multivariate Lag Operator Polynomials and Coefficient Constraints Interactively
- Estimate Vector Error-Correction Model Using Econometric Modeler
- Exploit Cointegrating Relationships to Impute Missing Data