random_ind_int creates a random GMAR, StMAR, or G-StMAR model compatible parameter vector.
smart_ind_int creates a random GMAR, StMAR, or G-StMAR model compatible parameter vector close to argument params.
random_ind_int(
p,
M,
model = c("GMAR", "StMAR", "G-StMAR"),
restricted = FALSE,
constraints = NULL,
mu_scale,
sigma_scale,
forcestat = FALSE
)smart_ind_int(
p,
M,
params,
model = c("GMAR", "StMAR", "G-StMAR"),
restricted = FALSE,
constraints = NULL,
mu_scale,
sigma_scale,
accuracy,
which_random,
forcestat = FALSE
)
Returns estimated parameter vector with the form described in initpop.
a positive integer specifying the autoregressive order of the model.
a positive integer specifying the number of mixture components.
a size (2x1) integer vector specifying the number of GMAR type components M1 in the
first element and StMAR type components M2 in the second element. The total number of mixture components is M=M1+M2.
is "GMAR", "StMAR", or "G-StMAR" model considered? In the 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 imposed to each regime's autoregressive parameters separately.
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 \(\psi\)\(=\psi_{1},...,\psi_{q}\).
The symbol \(\phi\) denotes an AR coefficient. Note that regardless of any constraints, the autoregressive order
is always 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 by taking absolute value) 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 \((M(p+3)+M-M1-1x1)\) vector \(\theta\)\(=\)(\(\upsilon_{1}\)\(,...,\)\(\upsilon_{M}\), \(\alpha_{1},...,\alpha_{M-1},\)\(\nu\)) where
\(\upsilon_{m}\)\(=(\phi_{m,0},\)\(\phi_{m}\)\(,\)\(\sigma_{m}^2)\)
\(\phi_{m}\)\(=(\phi_{m,1},...,\phi_{m,p}), m=1,...,M\)
\(\nu\)\(=(\nu_{M1+1},...,\nu_{M})\)
\(M1\) is the number of GMAR type regimes.
In the GMAR model, \(M1=M\) and the parameter \(\nu\) dropped. In the StMAR model, \(M1=0\).
If the model imposes linear constraints on the autoregressive parameters:
Replace the vectors \(\phi_{m}\) with the vectors \(\psi_{m}\) that satisfy
\(\phi_{m}\)\(=\)\(C_{m}\psi_{m}\) (see the argument constraints).
Size \((3M+M-M1+p-1x1)\) vector \(\theta\)\(=(\phi_{1,0},...,\phi_{M,0},\)\(\phi\)\(,\) \(\sigma_{1}^2,...,\sigma_{M}^2,\)\(\alpha_{1},...,\alpha_{M-1},\)\(\nu\)), where \(\phi\)=\((\phi_{1},...,\phi_{p})\) contains the AR coefficients, which are common for all regimes.
If the model imposes linear constraints on the autoregressive parameters:
Replace the vector \(\phi\) with the vector \(\psi\) that satisfies
\(\phi\)\(=\)\(C\psi\) (see the argument constraints).
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 the 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 mixing weight parameters \(\alpha\) are dropped, and in the case of StMAR or G-StMAR model,
the degrees of freedom parameters \(\nu\) 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 drawn from will be corresponding parameter
value divided by accuracy.
a numeric vector of maximum length M specifying which regimes should be random instead of "smart" when
using smart_ind. Does not affect mixing weight parameters. Default in none.
Monahan J.F. 1984. A Note on Enforcing Stationarity in Autoregressive-Moving Average Models. Biometrica 71, 403-404.