urca (version 1.3-4)

cajorls: OLS regression of VECM

Description

This function returns the OLS regressions of a restricted VECM, i.e. it returns a list object with elements of class `lm' containing the restricted VECM and a matrix object with the normalised cointegrating relationships. The user can provide a certain number of which equation in the VECM should be estimated and reported, or if "reg.number = NULL" each equation in the VECM will be estimated and its results are reported. Furthermore, the cointegratioon rank has to be supplied too.

Usage

cajorls(z, r = 1, reg.number = NULL)

Value

Returns a list object with elements of class lm for the restricted VECM and a matrix object with the normalised cointegrating vectors.

Arguments

z

An object of class ca.jo or cajo.test.

r

An integer, signifiying the cointegration rank.

reg.number

The number of the equation in the VECM that should be estimated or if set to NULL (the default), all equations within the VECM are estimated.

Author

Bernhard Pfaff

Details

The cointegration space is normalised as \(\bold{\beta}_c = \bold{\beta}(S'\bold{\beta})^{-1}\), with \(S' = (I_r, 0)\).

References

Johansen, S. (1995), Likelihood-Based Inference in Cointegrated Vector Autoregressive Models, Oxford University Press, Oxford.

Lütkepohl, H. (2006), New Introduction to Multiple Time Series Analysis, Springer, New York.

See Also

ca.jo, cajools, lm, ca.jo-class and urca-class.

Examples

data(finland)
sjf <- finland
sjf.vecm <- ca.jo(sjf, ecdet = "none", type = "eigen", K = 2,
spec = "longrun", season = 4)
sjf.vecm.rls <- cajorls(sjf.vecm, r = 2)
summary(sjf.vecm.rls$rlm)
sjf.vecm.rls$beta