get_Sigmas: Calculate the dp-dimensional covariance matrices Sigma_{m,p}...

In sstvars: Toolkit for Reduced Form and Structural Smooth Transition Vector Autoregressive Models

Calculate the dp-dimensional covariance matrices \Sigma_{m,p} in the transition weights with weight_function="relative_dens"

Description

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.

Usage

get_Sigmas(p, M, d, all_A, all_boldA, all_Omegas)

Arguments

p	a positive integer specifying the autoregressive order
M	a positive integer specifying the number of regimes
d	the number of time series in the system, i.e., the dimension
all_A	4D array containing all coefficient matrices A_{m,i}, obtained from pick_allA.
all_boldA	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.
all_Omegas	a [d, d, M] array containing the covariance matrix Omegas

Details

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.

Value

Returns a [dp, dp, M] array containing the dp-dimensional covariance matrices for each regime.

References

• 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.

sstvars documentation built on April 11, 2025, 5:47 p.m.