jcontest
Johansen constraint test
Syntax
Description
returns the rejection decisions h
= jcontest(Y
,r
,test
,Cons
)h
from conducting the Johansen
constraint test, which assesses linear constraints on either the error-correction
(adjustment) speeds A or the cointegration space spanned by the
cointegrating matrix B in the reduced-rank VEC(q) model of the multivariate time series
yt, where:
Y
is a matrix of observations of yt.r
is the common rank of matrices A and B.test
specifies the constraint types, including linear or equality constraints on A or B.Cons
specifies the test constraint values.
For a particular test, the constraint type and values form the null hypotheses tested against the alternative hypothesis H(r) of cointegration rank less than or equal to r (an unconstrained VEC model). The tests also produce maximum likelihood estimates of the parameters in the VEC(q) model, subject to the constraints.
Each element of test
and Cons
results in a
separate test.
returns the table StatTbl
= jcontest(Tbl
,r
,test
,Cons
)StatTbl
containing variables for the test results,
statistics, and settings from conducting the Johansen constraint test on all variables of
the input table or timetable Tbl
.
To select a subset of variables in Tbl
to test, use the
DataVariables
name-value argument.
[___] = jcontest(___,
specifies options using one or more name-value arguments in
addition to any of the input argument combinations in previous syntaxes.
Name=Value
)jcontest
returns the output argument combination for the
corresponding input arguments.
In addition to bp
, some options control the number of tests to
conduct.
For example, jcontest(Tbl,r,test,Cons,Model="H2",DataVariables=1:5)
tests the first 5 variables in the input table Tbl
using the Johansen
model that excludes all deterministic terms.
Examples
Input Arguments
Output Arguments
More About
Tips
jcontest
compares finite-sample statistics to asymptotic critical values, and tests can show significant size distortions for small samples [2]. Larger samples lead to more reliable inferences.To convert VEC(q) model parameters in the
mles
output to vector autoregressive (VAR) model parameters, use thevec2var
function.
Algorithms
jcontest
identifies deterministic terms that are outside of the cointegrating relations, c1 and d1, by projecting constant and linear regression coefficients, respectively, onto the orthogonal complement of A.The parameters A and B in the reduced-rank VEC(q) model are not identifiable.
jcontest
identifies B using the methods in [3], depending on the test.Tests on B answer questions about the space of cointegrating relations. Tests on A answer questions about common driving forces in the system. For example, an all-zero row in A indicates a variable that is weakly exogenous with respect to the coefficients in B. Such a variable can affect other variables, but it does not adjust to disequilibrium in the cointegrating relations. Similarly, a standard unit vector column in A indicates a variable that is exclusively adjusting to disequilibrium in a particular cointegrating relation.
Constraint matrices
R
satisfying R′A = 0 or R′B = 0 are equivalent to A = Hφ or B = Hφ, where H is the orthogonal complement of R (null(R')
) and φ is a vector of free parameters.
References
[1] Hamilton, James 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. Likelihood-Based 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.
Version History
Introduced in R2011a