pick_pars picks \(\phi_0\)/\(\mu\), ar-coefficient and variance parameters from parameter vector
pick_pars(p, M, params, model = c("GMAR", "StMAR", "G-StMAR"),
restricted = FALSE, constraints = NULL)a positive integer specifying the order of AR coefficients.
a positive integer specifying the number of mixture components.
a size (2x1) vector specifying the number of GMAR-type components M1 in the
first element and StMAR-type components M2 in the second. The total number of mixture components is M=M1+M2.
a real valued parameter vector specifying the model.
Size \((M(p+3)-1x1)\) vector \(\theta\)\(=\)(\(\upsilon_{1}\),...,\(\upsilon_{M}\), \(\alpha_{1},...,\alpha_{M-1}\)), where \(\upsilon_{m}\)\(=(\phi_{m,0},\)\(\phi_{m}\)\(, \sigma_{m}^2)\) and \(\phi_{m}\)=\((\phi_{m,1},...,\phi_{m,p}), m=1,...,M\).
Size \((M(p+4)-1x1)\) vector (\(\theta, \nu\))\(=\)(\(\upsilon_{1}\),...,\(\upsilon_{M}\), \(\alpha_{1},...,\alpha_{M-1}, \nu_{1},...,\nu_{M}\)).
Size \((M(p+3)+M2-1x1)\) vector (\(\theta, \nu\))\(=\)(\(\upsilon_{1}\),...,\(\upsilon_{M}\), \(\alpha_{1},...,\alpha_{M-1}, \nu_{M1+1},...,\nu_{M}\)).
Replace the vectors \(\phi_{m}\) with vectors \(\psi_{m}\) and provide a list of constraint matrices C that satisfy \(\phi_{m}\)\(=\)\(R_{m}\psi_{m}\) for all \(m=1,...,M\), where \(\psi_{m}\)\(=(\psi_{m,1},...,\psi_{m,q_{m}})\).
Size \((3M+p-1x1)\) vector \(\theta\)\(=(\phi_{1,0},...,\phi_{M,0},\)\(\phi\)\(, \sigma_{1}^2,...,\sigma_{M}^2,\alpha_{1},...,\alpha_{M-1})\), where \(\phi\)=\((\phi_{1},...,\phi_{M})\).
Size \((4M+p-1x1)\) vector (\(\theta, \nu\))\(=(\phi_{1,0},...,\phi_{M,0},\)\(\phi\)\(, \sigma_{1}^2,...,\sigma_{M}^2,\alpha_{1},...,\alpha_{M-1}, \nu_{1},...,\nu_{M})\).
Size \((3M+M2+p-1x1)\) vector (\(\theta, \nu\))\(=(\phi_{1,0},...,\phi_{M,0},\)\(\phi\)\(, \sigma_{1}^2,...,\sigma_{M}^2,\alpha_{1},...,\alpha_{M-1}, \nu_{M1+1},...,\nu_{M})\).
Replace the vector \(\phi\) with vector \(\psi\) and provide a constraint matrix \(C\) that satisfies \(\phi\)\(=\)\(R\psi\), where \(\psi\)\(=(\psi_{1},...,\psi_{q})\).
Symbol \(\phi\) denotes an AR coefficient, \(\sigma^2\) a variance, \(\alpha\) a mixing weight and \(\nu\) a degrees of
freedom parameter. If parametrization=="mean" just replace each intercept term \(\phi_{m,0}\) with regimewise mean
\(\mu_m = \phi_{m,0}/(1-\sum\phi_{i,m})\). In the G-StMAR model the first M1 components are GMAR-type
and the rest M2 components are StMAR-type.
Note that in the case M=1 the parameter \(\alpha\) is dropped, and in the case of StMAR or G-StMAR model
the degrees of freedom parameters \(\nu_{m}\) have to be larger than \(2\).
is "GMAR", "StMAR" or "G-StMAR" model considered? In G-StMAR model the first M1 components
are GMAR-type and the rest M2 components are StMAR-type.
a logical argument stating whether the AR coefficients \(\phi_{m,1},...,\phi_{m,p}\) are restricted to be the same for all regimes.
specifies linear constraints applied to the autoregressive parameters.
a list of size \((pxq_{m})\) constraint matrices \(C_{m}\) of full column rank satisfying \(\phi_{m}\)\(=\)\(C_{m}\psi_{m}\) for all \(m=1,...,M\), where \(\phi_{m}\)\(=(\phi_{m,1},...,\phi_{m,p})\) and \(\psi_{m}\)\(=(\psi_{m,1},...,\psi_{m,q_{m}})\).
a size \((pxq)\) constraint matrix \(C\) of full column rank satisfying \(\phi\)\(=\)\(C\psi\), where \(\phi\)\(=(\phi_{1},...,\phi_{p})\) and \(\psi\)\(=\psi_{1},...,\psi_{q}\).
Symbol \(\phi\) denotes an AR coefficient. Note that regardless of any constraints, the nominal order of AR coefficients is
alway p for all regimes.
Ignore or set to NULL if applying linear constraints is not desired.
Returns a \((Mx(p+2))\) matrix containing the parameters, column for each component. First row for \(\phi_0\) or \(\mu\) depending on the parametrization, second row for \(\phi_1\),..., second last row for \(\phi_p\) and last row for \(\sigma^2\).