weight_function="relative_dens"get_Sigmas calculatesthe dp-dimensional covariance matrices \(\Sigma_{m,p}\) in
the transition weights with weight_function="relative_dens" so that the algorithm proposed
by McElroy (2017) employed whenever it reduces the computation time.
get_Sigmas(p, M, d, all_A, all_boldA, all_Omegas)Returns a [dp, dp, M] array containing the dp-dimensional covariance matrices for each regime.
a positive integer specifying the autoregressive order
a positive integer specifying the number of regimes
the number of time series in the system, i.e., the dimension
4D array containing all coefficient matrices \(A_{m,i}\), obtained from pick_allA.
3D array containing the \(((dp)x(dp))\) "bold A" (companion form) matrices of each regime,
obtained from form_boldA. Will be computed if not given.
a [d, d, M] array containing the covariance matrix Omegas
Calculates the dp-dimensional covariance matrix using the formula (2.1.39) in Lütkepohl (2005) when
d*p < 12 and using the algorithm proposed by McElroy (2017) otherwise.
The code in the implementation of the McElroy's (2017) algorithm (in the function VAR_pcovmat) is
adapted from the one provided in the supplementary material of McElroy (2017). Reproduced under GNU General
Public License, Copyright (2015) Tucker McElroy.
Lütkepohl H. 2005. New Introduction to Multiple Time Series Analysis, Springer.
McElroy T. 2017. Computation of vector ARMA autocovariances. Statistics and Probability Letters, 124, 92-96.