Check the stationarity and invertibility of a fitted VARMA-LiNGAM model

Inspects the eigenvalues of the companion matrices of the reduced-form AR coefficients (Phi, stationarity) and MA coefficients (Theta, invertibility) stored in the result. The process is stationary when every AR eigenvalue lies strictly inside the unit circle, and invertible when every MA eigenvalue does; a modulus on or outside the circle signals a (near-)unit root or a non-invertible MA polynomial, under which the VARMA-LiNGAM estimates (and the residual filtering) are unreliable. Invertibility is worth checking here because the Hannan-Rissanen estimator does not enforce it.

Usage

check_varma_stationarity(result, tol = 1)

Arguments

result

a VARMALiNGAMResult from lingam_varma()

tol

threshold for the eigenvalue moduli (default 1)

Value

a varma_stationarity object (list) with ar_moduli / ma_moduli (sorted descending; empty when p = 0 / q = 0), max_ar_modulus, max_ma_modulus, is_stationary, is_invertible, order, and tol.

References

Stationarity diagnostics in the spirit of the VARLiNGAM R code of Moneta, A., Entner, D., Hoyer, P. O., & Coad, A. (2013), Oxford Bulletin of Economics and Statistics, 75(5), 705-730. https://sites.google.com/site/dorisentner/publications/VARLiNGAM

Examples

s <- generate_varmalingam_sample(n = 1000, seed = 42)
m <- lingam_varma(s$data,
  order = c(1, 1), criterion = NULL,
  reg_method = "ols", prune = FALSE
)
check_varma_stationarity(m)
#> === VARMA Stationarity / Invertibility Check ===
#> Order (p, q):         (1, 1)
#> Max |AR eigenvalue|:  0.4763  (threshold 1.00)
#> Stationary:           YES
#> Max |MA eigenvalue|:  0.2974  (threshold 1.00)
#> Invertible:           YES