urca (version 1.3-4)

alphaols: OLS regression of VECM weighting matrix

Description

This functions estimates the \(\bold{\alpha}\) matrix of a VECM. The following OLS regression of the R-form of the VECM is hereby utilised: $$\bold{R}_{0t} = \bold{\alpha}\bold{\beta}\prime \bold{R}_{kt} + \bold{\varepsilon}_t \qquad t=1, \dots, T$$

Usage

alphaols(z, reg.number = NULL)

Value

Returns an object of class lm.

Arguments

z

An object of class ca.jo.

reg.number

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

Author

Bernhard Pfaff

Details

The cointegrating relations, i.e. \(\bold{R}_{kt}\prime \bold{\beta}\) are calculated by using z@RK and z@V.

References

Johansen, S. (1988), Statistical Analysis of Cointegration Vectors, Journal of Economic Dynamics and Control, 12, 231--254.

Johansen, S. and Juselius, K. (1990), Maximum Likelihood Estimation and Inference on Cointegration -- with Applications to the Demand for Money, Oxford Bulletin of Economics and Statistics, 52, 2, 169--210.

Johansen, S. (1991), Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models, Econometrica, Vol. 59, No. 6, 1551--1580.

See Also

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

Examples

data(denmark)
sjd <- denmark[, c("LRM", "LRY", "IBO", "IDE")]
sjd.vecm1 <- ca.jo(sjd, ecdet = "const", type="eigen", K=2, spec="longrun",
season=4)
summary(alphaols(sjd.vecm1))
summary(alphaols(sjd.vecm1, reg.number=1))