check_Bt_Cpp

This internal function takes a cube of matrices (<code>all_Omegas</code>),
a matrix of weights (<code>alpha_mt</code>), and a numerical tolerance (<code>posdef_tol</code>)
to check the invertibility of weighted sums of the matrices in the cube. For each row
in <code>alpha_mt</code>, it computes a weighted sum of matrices, and checks if this sum is
invertible by verifying that its determinant is not within the specified tolerance of zero.

internal

Penalized and non-penalized maximum likelihood estimation of smooth
transition vector autoregressive models with various types of transition weight
functions, conditional distributions, and identification methods. Constrained
estimation with various types of constraints is available. Residual based
model diagnostics, forecasting, simulations, and calculation of impulse
response functions, generalized impulse response functions, and generalized
forecast error variance decompositions. See
Heather Anderson, Farshid Vahid (1998) <doi:10.1016/S0304-4076(97)00076-6>,
Helmut Lütkepohl, Aleksei Netšunajev (2017) <doi:10.1016/j.jedc.2017.09.001>,
Markku Lanne, Savi Virolainen (2025) <doi:10.48550/arXiv.2403.14216>,
Savi Virolainen (2025) <doi:10.48550/arXiv.2404.19707>.

Savi Virolainen

sstvars

Toolkit for Reduced Form and Structural Smooth Transition Vector
Autoregressive Models

check_Bt_Cpp function

<dl><dt>all_Omegas</dt>
<dd>A cube (3D array) of impact matrices, with each slice being an inveritble square matrix.</dd>
<dt>alpha_mt</dt>
<dd>A matrix of weights, with as many columns as there are slices in <code>all_Omegas</code>.</dd>
<dt>posdef_tol</dt>
<dd>A strictly positive small number used as a tolerance for checking
the invertibility of the matrix. The matrix is considered non-invertible if
its determinant is less than this tolerance.</dd></dl>

Arguments

Check Matrix B Invertibility with C++ (Internal Function) — check_Bt_Cpp

<dl>

<dt>all_Omegas</dt>
<dd>A cube (3D array) of impact matrices, with each slice being an inveritble square matrix.</dd>


<dt>alpha_mt</dt>
<dd>A matrix of weights, with as many columns as there are slices in <code>all_Omegas</code>.</dd>


<dt>posdef_tol</dt>
<dd>A strictly positive small number used as a tolerance for checking
the invertibility of the matrix. The matrix is considered non-invertible if
its determinant is less than this tolerance.</dd>

</dl>

check_Bt_Cpp: Check Matrix B Invertibility with C++ (Internal Function)

Description

Usage

Value

Arguments