get_Sigmas calculates the dp-dimensional covariance matrices \(\Sigma_{m,p}\)
in the mixing weights of the GMVAR, StMVAR, or G-StMVAR 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)Returns a [dp, dp, M] array containing the dp-dimensional covariance matrices for each regime.
a positive integer specifying the autoregressive order of the model.
a positive integer specifying the number of mixture components.
a size \((2\times 1)\) integer vector specifying the number of GMVAR type components M1
in the first element and StMVAR type components M2 in the second element. The total number of mixture components
is M=M1+M2.
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 \(((dp)\times (dp))\) "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
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.
Kalliovirta L., Meitz M. and Saikkonen P. 2016. Gaussian mixture vector autoregression. Journal of Econometrics, 192, 485-498.
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.
Virolainen S. 2022. Structural Gaussian mixture vector autoregressive model with application to the asymmetric effects of monetary policy shocks. Unpublished working paper, available as arXiv:2007.04713.
Virolainen S. 2022. Gaussian and Student's t mixture vector autoregressive model with application to the asymmetric effects of monetary policy shocks in the Euro area. Unpublished working paper, available as arXiv:2109.13648.