R: OLS regression of VECM

cajorls {urca} | R Documentation

## 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)

### 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.

### Details

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

### Value

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

### Author(s)

Bernhard Pfaff

### 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

[Package urca version 1.3-0 Index]