vars (version 1.5-3)

roots: 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.

Value

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

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:

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

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.

References

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

L<U+34AE5C2F>hl, H. (2006), New Introduction to Multiple Time Series Analysis, Springer, New York.

See Also

VAR

Examples

# NOT RUN {
data(Canada)
var.2c <- VAR(Canada, p = 2, type = "const")
roots(var.2c)
# }