randomIndividual_int creates a random GMAR, StMAR or G-StMAR model compatible parameter vector.
smartIndividual_int creates a random GMAR, StMAR or G-StMAR model compatible parameter vector close to argument params.
randomIndividual_int(p, M, model = c("GMAR", "StMAR", "G-StMAR"),
restricted = FALSE, constraints = NULL, meanscale, sigmascale,
forcestat = FALSE)smartIndividual_int(p, M, params, model = c("GMAR", "StMAR", "G-StMAR"),
restricted = FALSE, constraints = NULL, meanscale, sigmascale,
accuracy, whichRandom, forcestat = FALSE)
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.
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.
a real valued vector of length two specifying the mean (the first element) and standard deviation (the second element) of the normal distribution from which the \(\phi_{m,0}\) or \(\mu_{m}\) (depending on the desired parametrization) parameters (for random regimes) should be generated.
a positive real number specifying the standard deviation of the (zero mean, positive only) normal distribution from which the component variance parameters (for random regimes) should be generated.
use the algorithm by Monahan (1984) to force stationarity on the AR parameters (slower) for random regimes? Not supported for constrained models.
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 \(2\).
a real number larger than zero specifying how close to params the generated parameter vector should be.
Standard deviation of the normal distribution from which new parameter values are drawed from will be corresponding parameter value divided by accuracy.
an (optional) numeric vector of max length M specifying which regimes should be random instead of "smart" when
using smartIndividual. Does not affect on mixing weight parameters. Default in none.
Returns estimated parameter vector described in initpop.
Monahan J.F. 1984. A Note on Enforcing Stationarity in Autoregressive-Moving Average Models. Biometrica 71, 403-404.