Student_densities_Cpp

Calculates logs of multivariate Student t densities with varying mean
 and varying covariance matrix AND EXCLUDING the constant term of the density
 (the constant is calculated and added in R code). The varying conditional covariance
 matrix is calculated within the function from the regime covariance matrices and
 transition weights.

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, counterfactual analysis, and
computation of impulse response functions, generalized impulse response functions,
generalized forecast error variance decompositions, as well as historical
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

Student_densities_Cpp function

<dl><dt>obs</dt>
<dd>a \((T \times d)\) matrix such that the \(i\)th row contains the vector
\(y_{i}=(y_{1i},...,y_{di})\) \((dx1)\). That is, the initial values are
excluded but the last observations is included.</dd>
<dt>means</dt>
<dd>a \((T \times d)\) matrix such that the \(i\)th row contains the
conditional mean of the process \(\mu_{y,i}\).</dd>
<dt>covmats</dt>
<dd>a \((d \times d \times M)\) array such that the slice <code>[, , m]</code>
contains the conditional covariance matrix of regime m.</dd>
<dt>alpha_mt</dt>
<dd>a \((T \times M)\) matrix such that <code>[t, m]</code> contains the time t
transition weights of the \(m\)th regime.</dd>
<dt>df</dt>
<dd>the degrees of freedom parameter value (assumed larger than two).</dd></dl>

Arguments

Calculate log multivariate Student's t densities — Student_densities_Cpp

<dl>

<dt>obs</dt>
<dd>a \((T \times d)\) matrix such that the \(i\)th row contains the vector
\(y_{i}=(y_{1i},...,y_{di})\) \((dx1)\). That is, the initial values are
excluded but the last observations is included.</dd>


<dt>means</dt>
<dd>a \((T \times d)\) matrix such that the \(i\)th row contains the
conditional mean of the process \(\mu_{y,i}\).</dd>


<dt>covmats</dt>
<dd>a \((d \times d \times M)\) array such that the slice <code>[, , m]</code>
contains the conditional covariance matrix of regime m.</dd>


<dt>alpha_mt</dt>
<dd>a \((T \times M)\) matrix such that <code>[t, m]</code> contains the time t
transition weights of the \(m\)th regime.</dd>


<dt>df</dt>
<dd>the degrees of freedom parameter value (assumed larger than two).</dd>

</dl>

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Student_densities_Cpp: Calculate log multivariate Student's t densities

Description

Usage

Value

Arguments

Details