vars (version 1.1-9)

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).

encoding

latin1

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�tkepohl, 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)