R: Eigenvalues of the companion coefficient matrix of a...

roots {vars} | R Documentation

## Eigenvalues of the companion coefficient matrix of a VAR(p)-process

### Description

Returns a vector of the eigenvalues of the companion coefficient matrix.

### Usage

    roots(x, modulus = TRUE)

### Arguments

`x` | An object of class ‘`varest`’, generated by `VAR()`.
`modulus` | Logical, set to `TRUE` for returning the modulus.

### Details

Any VAR(p)-process can be written in a first-order vector autoregressive form: the companion form. A VAR(p)-process is stable, if its reverse characteristic polynomial:

\det(I_K - A_1 z - \cdots - A_p z^p) \neq 0 \; \hbox{for} \; |z| ≤ 1 \; ,

has no roots in or on the complex circle. This is equivalent to the condition that all eigenvalues of the companion matrix A have modulus less than 1. The function `roots()`, does compute the eigen values of the companion matrix A and returns by default their moduli.

### Value

A vector object with the eigen values of the companion matrix, or their moduli (default).

### Author(s)

Bernhard Pfaff

### References

Hamilton, J. (1994), Time Series Analysis, Princeton University Press, Princeton.

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

### See Also

`VAR`

### Examples

    data(Canada)
    var.2c <- VAR(Canada, p = 2, type = "const")
    roots(var.2c)

[Package vars version 1.5-3 Index]