Johansen constraint test
[h,pValue,stat,cValue,mles]
= jcontest(Y,r,test,Cons)
[h,pValue,stat,cValue,mles] = jcontest(Y,r,test,Cons,Name,Value)
jcontest
tests linear constraints on either
the errorcorrection speeds A or the cointegration
space spanned by B in the reducedrank VEC(q)
model of y_{t}:
$$\Delta {y}_{t}=A{B}^{\prime}{y}_{t1}+{B}_{1}\Delta {y}_{t1}+\dots +{B}_{q}\Delta {y}_{tq}+DX+{\epsilon}_{t}.$$
Null hypotheses specifying constraints on A or B are tested against the alternative H(r) of cointegration rank less than or equal to r, without the constraints. The tests also produce maximum likelihood estimates of the parameters in the VEC(q) model, subject to the constraints.
[
performs
the Johansen constraint test on a data matrix h
,pValue
,stat
,cValue
,mles
]
= jcontest(Y
,r
,test
,Cons
)Y
.
[
performs
the Johansen constraint test on a data matrix h
,pValue
,stat
,cValue
,mles
] = jcontest(Y
,r
,test
,Cons
,Name,Value
)Y
with
additional options specified by one or more Name,Value
pair
arguments.

 

Scalar or vector of integers between 1 and  

String or cell vector of strings specifying the type of tests to be performed. Values are:
 

Matrix or cell vector of matrices specifying test constraints.
For constraints on B, the number of rows in each
matrix,

Specify optional commaseparated pairs of Name,Value
arguments.
Name
is the argument
name and Value
is the corresponding
value. Name
must appear
inside single quotes (' '
).
You can specify several name and value pair
arguments in any order as Name1,Value1,...,NameN,ValueN
.

String or cell vector of strings specifying the form of the
deterministic components of the VEC(q) model of y_{t}.
Values of
Deterministic terms outside of the cointegrating relations, c_{1} and d_{1}, are identified by projecting constant and linear regression coefficients, respectively, onto the orthogonal complement of A.  

Scalar or vector of nonnegative integers indicating the number q of lagged differences in the VEC(q) model of y_{t}. Lagging and differencing a time series reduce the sample size. Absent any presample values, if y_{t} is defined for t = 1:N, then the lagged series y_{t−k} is defined for t = k+1:N. Differencing reduces the time base to k+2:N. With q lagged differences, the common time base is q+2:N and the effective sample size is T = N − (q+1). Default: 0  

Scalar or vector of nominal significance levels for the tests.
Values must be greater than zero and less than one. The default value
is 
Singleelement values for inputs are expanded to the length of any vector value (the number of tests). Vector values must have equal length. If any value is a row vector, all outputs are row vectors.

Vector of Boolean decisions for the tests, with length equal
to the number of tests. Values of  

Vector of righttail probabilities of the test statistics, with length equal to the number of tests.  

Vector of test statistics, with length equal to the number of tests. Statistics are likelihood ratios determined by the test.  

Critical values for righttail probabilities, with length equal to the number of tests. The asymptotic distributions of the test statistics are chisquare, with the degreeoffreedom parameter determined by the test.  

Structure of maximum likelihood estimates associated with the VEC(q) model of y_{t}, subject to the constraints. Each structure has the following fields:

[1] Hamilton, J. D. Time Series Analysis. Princeton, NJ: Princeton University Press, 1994.
[2] Haug, A. "Testing Linear Restrictions on Cointegrating Vectors: Sizes and Powers of Wald Tests in Finite Samples." Econometric Theory. v. 18, 2002, pp. 505–524.
[3] Johansen, S. LikelihoodBased Inference in Cointegrated Vector Autoregressive Models. Oxford: Oxford University Press, 1995.
[4] Juselius, K. The Cointegrated VAR Model. Oxford: Oxford University Press, 2006.
[5] Morin, N. "Likelihood Ratio Tests on Cointegrating Vectors, Disequilibrium Adjustment Vectors, and their Orthogonal Complements." European Journal of Pure and Applied Mathematics. v. 3, 2010, pp. 541–571.