randomIndividual: DEPRECATED, USE 'random_ind' OR 'smart_ind' INSTEAD! Create...

In uGMAR: Estimate Univariate Gaussian and Student's t Mixture Autoregressive Models

DEPRECATED, USE random_ind OR smart_ind INSTEAD! Create random GMAR, StMAR, or G-StMAR model compatible parameter vector

Description

randomIndividual creates a random GMAR, StMAR, or G-StMAR model compatible mean-parametrized parameter vector. DEPRECATED, USE random_ind INSTEAD!

smartIndividual creates a random GMAR, StMAR, or G-StMAR model compatible parameter vector close to argument params. Sometimes returns exactly the given parameter vector. DEPRECATED, USE smart_ind INSTEAD!

Usage

randomIndividual(
  p,
  M,
  model = c("GMAR", "StMAR", "G-StMAR"),
  restricted = FALSE,
  constraints = NULL,
  mu_scale,
  sigma_scale,
  forcestat = FALSE,
  meanscale = NULL,
  sigmascale = NULL
)

smartIndividual(
  p,
  M,
  params,
  model = c("GMAR", "StMAR", "G-StMAR"),
  restricted = FALSE,
  constraints = NULL,
  mu_scale,
  sigma_scale,
  accuracy,
  which_random = numeric(0),
  forcestat = FALSE,
  whichRandom = NULL,
  meanscale = NULL,
  sigmascale = NULL
)

Arguments

p	a positive integer specifying the autoregressive order of the model.
M	For GMAR and StMAR models: a positive integer specifying the number of mixture components. For G-StMAR models: 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.
model	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.
restricted	a logical argument stating whether the AR coefficients \phi_{m,1},...,\phi_{m,p} are restricted to be the same for all regimes.
constraints	specifies linear constraints imposed to each regime's autoregressive parameters separately. For non-restricted models: 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}}). For restricted models: 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.
mu_scale	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.
sigma_scale	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.
forcestat	use the algorithm by Monahan (1984) to force stationarity on the AR parameters (slower) for random regimes? Not supported for constrained models.
meanscale	deprecated! Use mu_scale instead!
sigmascale	deprecated! Use sigma_scale instead!
params	a real valued parameter vector specifying the model. For non-restricted models: 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). For restricted models: 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.
accuracy	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.
which_random	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.
whichRandom	deprecated! Use which_random instead!

Details

DEPRECATED, USE random_ind OR smart_ind INSTEAD!

These functions can be used, for example, to create initial populations for the genetic algorithm. Mean-parametrization (instead of intercept terms \phi_{m,0}) is assumed.

Value

Returns estimated parameter vector with the form described in initpop.

References

• Monahan J.F. 1984. A Note on Enforcing Stationarity in Autoregressive-Moving Average Models. Biometrica 71, 403-404.

uGMAR documentation built on Aug. 19, 2023, 5:10 p.m.