get_Sigmas {sstvars}R Documentation

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


[Package sstvars version 1.1.2 Index]