Johansen cointegration test
[h,pValue,stat,cValue,mles]
= jcitest(Y)
[h,pValue,stat,cValue,mles]
= jcitest(Y,Name,Value)
Johansen tests assess the null hypothesis H(r) of
cointegration rank less than or equal to r among
the numDims
dimensional time series in Y
against
alternatives H(numDims
) (trace
test)
or H(r+1) (maxeig
test).
The tests also produce maximum likelihood estimates of the parameters
in a vector errorcorrection (VEC) model of the cointegrated series.
[
performs the Johansen
cointegration test on a data matrix h
,pValue
,stat
,cValue
,mles
]
= jcitest(Y
)Y
.
[
performs
the Johansen cointegration test on a data matrix h
,pValue
,stat
,cValue
,mles
]
= jcitest(Y
,Name,Value
)Y
with
additional options specified by one or more Name,Value
pair
arguments.


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}: $$\Delta {y}_{t}=C{y}_{t1}+{B}_{1}\Delta {y}_{t1}+\dots +{B}_{q}\Delta {y}_{tq}+DX+{\epsilon}_{t}$$ If r < 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  

String or cell vector of strings indicating the type of test
to be performed. Values are
 

Scalar or vector of nominal significance levels for the tests. Values must be between 0.001 and 0.999. Default: 0.05  

String or cell vector of strings indicating whether or not to display a summary of test results and parameter estimates in the Command Window.
Scalar or single string values are expanded to the length of any vector value (the number of tests). Vector values must have equal length. 

Rows of Values of  

Rows of  

Rows of  

Rows of  

Rows of 
[1] Hamilton, J. D. Time Series Analysis. Princeton, NJ: Princeton University Press, 1994.
[2] Johansen, S. LikelihoodBased Inference in Cointegrated Vector Autoregressive Models. Oxford: Oxford University Press, 1995.
[3] MacKinnon, J. G., A. A. Haug, and L. Michelis. "Numerical Distribution Functions of Likelihood Ratio Tests for Cointegration." Journal of Applied Econometrics. v. 14, 1999, pp. 563–577.
[4] 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.