get_Sigmas calculates the dp-dimensional covariance matrices \(\Sigma_{m,p}\)
in the mixing weights of the GMVAR model 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_Omega)a positive integer specifying the autoregressive order of the model.
a positive integer specifying the number of mixture components.
the number of time series in the system.
4D array containing all coefficient matrices \(A_{m,i}\), obtained from pick_allA.
3D array containing the \(((dp)x(dp))\) "bold A" matrices related to each mixture component VAR-process,
obtained from form_boldA. Will be computed if not given.
a [d, d, M] array containing the covariance matrix Omegas
Returns a [dp, dp, M] array containing the dp-dimensional covariance matrices for each regime.
Calculates the dp-dimensional covariance matrix using the formula (2.1.39) in L<U+00FC>tkepohl (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.
Kalliovirta L., Meitz M. and Saikkonen P. 2016. Gaussian mixture vector autoregression. Journal of Econometrics, 192, 485-498.
L<U+00FC>tkepohl 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.