change_regime changes the regime parameters
\((\phi_{m},vec(A_{m,1}),...,\vec(A_{m,p}),vech(\Omega_m))\) (replace \(vech(\Omega_m)\)
by \(vec(B_m)\) for cond_dist="ind_Student")
of the given regime to the new given parameters.
change_regime(
p,
M,
d,
params,
m,
regime_pars,
cond_dist = c("Gaussian", "Student", "ind_Student", "ind_skewed_t")
)Returns parameter vector with m:th regime changed to regime_pars.
the autoregressive order of the model
the number of regimes
the number of time series in the system, i.e., the dimension
a real valued vector specifying the parameter values. Should have the form \(\theta = (\phi_{1},...,\phi_{M},\varphi_1,...,\varphi_M,\sigma,\alpha,\nu)\), where (see exceptions below):
\(\phi_{m} = \) the \((d \times 1)\) intercept (or mean) vector of the \(m\)th regime.
\(\varphi_m = (vec(A_{m,1}),...,vec(A_{m,p}))\) \((pd^2 \times 1)\).
cond_dist="Gaussian" or "Student":\(\sigma = (vech(\Omega_1),...,vech(\Omega_M))\) \((Md(d + 1)/2 \times 1)\).
cond_dist="ind_Student" or "ind_skewed_t":\(\sigma = (vec(B_1),...,vec(B_M)\) \((Md^2 \times 1)\).
\(\alpha = \) the \((a\times 1)\) vector containing the transition weight parameters (see below).
cond_dist = "Gaussian"):Omit \(\nu\) from the parameter vector.
cond_dist="Student":\(\nu > 2\) is the single degrees of freedom parameter.
cond_dist="ind_Student":\(\nu = (\nu_1,...,\nu_d)\) \((d \times 1)\), \(\nu_i > 2\).
cond_dist="ind_skewed_t":\(\nu = (\nu_1,...,\nu_d,\lambda_1,...,\lambda_d)\) \((2d \times 1)\), \(\nu_i > 2\) and \(\lambda_i \in (0, 1)\).
For models with...
weight_function="relative_dens":\(\alpha = (\alpha_1,...,\alpha_{M-1})\) \((M - 1 \times 1)\), where \(\alpha_m\) \((1\times 1), m=1,...,M-1\) are the transition weight parameters.
weight_function="logistic":\(\alpha = (c,\gamma)\) \((2 \times 1)\), where \(c\in\mathbb{R}\) is the location parameter and \(\gamma >0\) is the scale parameter.
weight_function="mlogit":\(\alpha = (\gamma_1,...,\gamma_M)\) \(((M-1)k\times 1)\), where \(\gamma_m\) \((k\times 1)\), \(m=1,...,M-1\) contains the multinomial logit-regression coefficients of the \(m\)th regime. Specifically, for switching variables with indices in \(I\subset\lbrace 1,...,d\rbrace\), and with \(\tilde{p}\in\lbrace 1,...,p\rbrace\) lags included, \(\gamma_m\) contains the coefficients for the vector \(z_{t-1} = (1,\tilde{z}_{\min\lbrace I\rbrace},...,\tilde{z}_{\max\lbrace I\rbrace})\), where \(\tilde{z}_{i} =(y_{it-1},...,y_{it-\tilde{p}})\), \(i\in I\). So \(k=1+|I|\tilde{p}\) where \(|I|\) denotes the number of elements in \(I\).
weight_function="exponential":\(\alpha = (c,\gamma)\) \((2 \times 1)\), where \(c\in\mathbb{R}\) is the location parameter and \(\gamma >0\) is the scale parameter.
weight_function="threshold":\(\alpha = (r_1,...,r_{M-1})\) \((M-1 \times 1)\), where \(r_1,...,r_{M-1}\) are the threshold values.
weight_function="exogenous":Omit \(\alpha\) from the parameter vector.
identification="heteroskedasticity":\(\sigma = (vec(W),\lambda_2,...,\lambda_M)\), where \(W\) \((d\times d)\) and \(\lambda_m\) \((d\times 1)\), \(m=2,...,M\), satisfy \(\Omega_1=WW'\) and \(\Omega_m=W\Lambda_mW'\), \(\Lambda_m=diag(\lambda_{m1},...,\lambda_{md})\), \(\lambda_{mi}>0\), \(m=2,...,M\), \(i=1,...,d\).
Above, \(\phi_{m}\) is the intercept parameter, \(A_{m,i}\) denotes the \(i\)th coefficient matrix of the \(m\)th
regime, \(\Omega_{m}\) denotes the positive definite error term covariance matrix of the \(m\)th regime, and \(B_m\)
is the invertible \((d\times d)\) impact matrix of the \(m\)th regime. \(\nu_m\) is the degrees of freedom parameter
of the \(m\)th regime. If parametrization=="mean", just replace each \(\phi_{m}\) with regimewise mean
\(\mu_{m}\).
which regime?
cond_dist="Gaussian" or cond_dist="Student":rhe \((dp + pd^2 + d(d+1)/2)\) vector \((\phi_{m},vec(A_{m,1}),...,\vec(A_{m,p}),vech(\Omega_m))\).
cond_dist="ind_Student" or "ind_skewed_t":the \((dp + pd^2 + d^2 + 1)\) vector \((\phi_{m},vec(A_{m,1}),...,\vec(A_{m,p}),vec(B_m))\).
Does not support constrained models or structural models. Weight parameters and distribution parameters are not changed.
Kheifets I.L., Saikkonen P.J. 2020. Stationarity and ergodicity of Vector STAR models. Econometric Reviews, 39:4, 407-414.
Lütkepohl H. 2005. New Introduction to Multiple Time Series Analysis, Springer.
Lanne M., Virolainen S. 2025. A Gaussian smooth transition vector autoregressive model: An application to the macroeconomic effects of severe weather shocks. Unpublished working paper, available as arXiv:2403.14216.
Virolainen S. 2025. Identification by non-Gaussianity in structural threshold and smooth transition vector autoregressive models. Unpublished working paper, available as arXiv:2404.19707.
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