Poles and Zeroes

Compute the poles and zeroes of VARMA and Statespace models. Note that these models describe the corresponding processes as $$x_t = k(B) u_t$$ where \((u_t)\) is a white noise process and \(k(B)\) is a rational filter (\(B\) denotes the lag- or backward shift operator). The poles and zeroes are the poles and zeroes of the rational transfer function \(k(z)\) of this filter.

Usage

# S3 method for armamod
zeroes(x, tol = sqrt(.Machine$double.eps), print_message = TRUE, ...)

# S3 method for armamod
poles(x, tol = sqrt(.Machine$double.eps), print_message = TRUE, ...)

# S3 method for rmfdmod
zeroes(x, tol = sqrt(.Machine$double.eps), print_message = TRUE, ...)

# S3 method for rmfdmod
poles(x, tol = sqrt(.Machine$double.eps), print_message = TRUE, ...)

# S3 method for stspmod
zeroes(x, tol = sqrt(.Machine$double.eps), print_message = TRUE, ...)

# S3 method for stspmod
poles(x, tol = sqrt(.Machine$double.eps), print_message = TRUE, ...)

Arguments

x

an object which represents a VARMA, RMFD or statespace model (i.e. an armamod(), rmfdmod() or stspmod() object).

tol

Double. Default set to sqrt(.Machine$double.eps). Required to decide on when a root is to be considered "at infinity".

print_message

Boolean. Default set to TRUE. Prints a message if roots "at infinity " are discarded.

...

not used.

Value

Vector of poles, respectively zeroes.

See also

For more details we refer to the discussion about the computation of poles and zeros of rational matrices in the companion package, see rationalmatrices::poles and zeroes.