pick_phi0 picks the intercept or mean parameters from the given parameter vector.
pick_phi0(M, d, params)Returns a \((d\times M)\) matrix containing \(\phi_{m,0}\) in the m:th column or
\(\mu_{m}\) if the parameter vector is mean-parametrized, \(, m=1,..,M\).
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 \(\theta = (\phi_{1,0},...,\phi_{M,0},\varphi_1,...,\varphi_M,\sigma,\alpha,\nu)\), where (see exceptions below):
\(\phi_{m,0} = \) 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, \(\phi_{m,0}\) 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 \(\phi_{m,0}\) with regimewise mean
\(\mu_{m}\).
No argument checks!
Does not support constrained parameter vectors.