ca.jo-class {urca} | R Documentation

## Representation of class ca.jo

### Description

This class contains the relevant information by applying the Johansen procedure to a matrix of time series data.

### Slots

`x`:
  Object of class `"ANY"`: A data matrix, or an object that can be coerced to it.
`Z0`:
  Object of class `"matrix"`: The matrix of the differenced series.
`Z1`:
  Object of class `"matrix"`: The regressor matrix, except for the lagged variables in levels.
`ZK`:
  Object of class `"matrix"`: The matrix of the lagged variables in levels.
`type`:
  Object of class `"character"`: The type of the test, either `"trace"` or `"eigen"`.
`model`:
  Object of class `"character"`: The model description in prose, with respect to the inclusion of a linear trend.
`ecdet`:
  Object of class `"character"`: Specifies the deterministic term to be included in the cointegration relation. This can be either "none", "const", or "trend".
`lag`:
  Object of class `"integer"`: The lag order for the variables in levels.
`P`:
  Object of class `"integer"`: The count of variables.
`season`:
  Object of class `"ANY"`: The frequency of the data, if seasonal dummies should be included, otherwise NULL.
`dumvar`:
  Object of class `"ANY"`: A matrix containing dummy variables. The row dimension must be equal to `x`, otherwise NULL.
`cval`:
  Object of class `"ANY"`: The critical values of the test at the 1%, 5% and 10% level of significance.
`teststat`:
  Object of class `"ANY"`: The values of the test statistics.
`lambda`:
  Object of class `"vector"`: The eigenvalues.
`Vorg`:
  Object of class `"matrix"`: The matrix of eigenvectors, such that hat V'S_{kk}hat V = I.
`V`:
  Object of class `"matrix"`: The matrix of eigenvectors, normalised with respect to the first variable.
`W`:
  Object of class `"matrix"`: The matrix of loading weights.
`PI`:
  Object of class `"matrix"`: The coeffcient matrix of the lagged variables in levels.
`DELTA`:
  Object of class `"matrix"`: The variance/covarinace matrix of `V`.
`GAMMA`:
  Object of class `"matrix"`: The coeffecient matrix of `Z1`.
`R0`:
  Object of class `"matrix"`: The matrix of residuals from the regressions in differences.
`RK`:
  Object of class `"matrix"`: The matrix of residuals from the regression in lagged levels.
`bp`:
  Object of class `"ANY"`: Potential break point, only set if function `cajolst` is called, otherwise `NA`.
`test.name`:
  Object of class `"character"`: The name of the test, i.e. `Johansen-Procedure'.
`spec`:
  Object of class `"character"`: The specification of the VECM.
`call`:
  Object of class `"call"`: The call of function `ca.jo`.

### Extends

Class `urca`, directly.

### Methods

Type `showMethods(classes="ca.jo")` at the R prompt for a complete list of methods which are available for this class.

Useful methods include

`show`:
  test statistic.
`summary`:
  like show, but critical values, eigenvectors and loading matrix added.
`plot`:
  The series of the VAR and their potential cointegration relations.

### 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`, `plotres` and `urca-class`.

[Package urca version 1.2-3 Index]