Verifies whether autoregressive coefficients satisfy stationarity conditions by checking that all roots of the characteristic polynomial lie outside the unit circle.
check_stationarity(phi)A list with:
Logical indicating whether the process is stationary
Complex roots of the characteristic polynomial
Moduli of the roots
Numeric vector of AR coefficients (phi_1, phi_2, ..., phi_p).
For an AR(p) process, stationarity requires that all roots of the characteristic polynomial \(1 - \phi_1 z - \phi_2 z^2 - ... - \phi_p z^p\) have modulus greater than 1. This is equivalent to requiring that all roots of the polynomial lie outside the unit circle in the complex plane.
The function constructs the companion matrix and computes its eigenvalues, which are the inverses of the characteristic polynomial roots.
Hamilton, J. D. (1994). Time Series Analysis. Princeton University Press. Chapter 1.