get_Sigmas

<code>get_Sigmas</code> calculatesthe dp-dimensional covariance matrices \(\Sigma_{m,p}\) in
 the transition weights with <code>weight_function="relative_dens"</code> so that the algorithm proposed
 by McElroy (2017) employed whenever it reduces the computation time.

internal

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 (2024) <doi:10.48550/arXiv.2403.14216>,
Savi Virolainen (2024) <doi:10.48550/arXiv.2404.19707>.

Savi Virolainen

sstvars

Toolkit for Reduced Form and Structural Smooth Transition Vector
Autoregressive Models

get_Sigmas function

<dl><dt>p</dt>
<dd>a positive integer specifying the autoregressive order</dd>
<dt>M</dt>
<dd>a positive integer specifying the number of regimes</dd>
<dt>d</dt>
<dd>the number of time series in the system, i.e., the dimension</dd>
<dt>all_A</dt>
<dd>4D array containing all coefficient matrices \(A_{m,i}\), obtained from <code>pick_allA</code>.</dd>
<dt>all_boldA</dt>
<dd>3D array containing the \(((dp)x(dp))\) "bold A" (companion form) matrices of each regime,
obtained from <code>form_boldA</code>. Will be computed if not given.</dd>
<dt>all_Omegas</dt>
<dd>a <code>[d, d, M]</code> array containing the covariance matrix Omegas</dd></dl>

Arguments

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

<dl>

<dt>p</dt>
<dd>a positive integer specifying the autoregressive order</dd>


<dt>M</dt>
<dd>a positive integer specifying the number of regimes</dd>


<dt>d</dt>
<dd>the number of time series in the system, i.e., the dimension</dd>


<dt>all_A</dt>
<dd>4D array containing all coefficient matrices \(A_{m,i}\), obtained from <code>pick_allA</code>.</dd>


<dt>all_boldA</dt>
<dd>3D array containing the \(((dp)x(dp))\) "bold A" (companion form) matrices of each regime,
obtained from <code>form_boldA</code>. Will be computed if not given.</dd>


<dt>all_Omegas</dt>
<dd>a <code>[d, d, M]</code> array containing the covariance matrix Omegas</dd>

</dl>

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

Description

Usage

Value

Arguments

Details

References