R: OLS regression of VECM weighting matrix

alphaols {urca} | R Documentation

## OLS regression of VECM weighting matrix

### Description

This functions estimates the \bold{α} matrix of a VECM. The following OLS regression of the R-form of the VECM is hereby utilised:

\bold{R}_{0t} = \bold{α}\bold{β}\prime \bold{R}_{kt} + \bold{\varepsilon}_t \qquad t=1, …, T

### Usage

    alphaols(z, reg.number = NULL)

### 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.

### Details

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

### Value

Returns an object of class `lm`.

### Author(s)

Bernhard Pfaff

### 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))

[Package urca version 1.3-0 Index]