Eigenvalues of the companion coefficient matrix of a VAR(p)-process
Returns a vector of the eigenvalues of the companion coefficient matrix.
roots(x, modulus = TRUE)
x |
An object of class ‘ |
modulus |
Logical, set to |
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.
A vector object with the eigen values of the companion matrix, or their moduli (default).
Bernhard Pfaff
Hamilton, J. (1994), Time Series Analysis, Princeton University Press, Princeton.
Lütkepohl, H. (2006), New Introduction to Multiple Time Series Analysis, Springer, New York.
data(Canada) var.2c <- VAR(Canada, p = 2, type = "const") roots(var.2c)
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