reform_parameters: Reform any parameter vector into standard form.

Description

reform_parameters takes a parameter vector of any (non-constrained) GMAR, StMAR, or G-StMAR model and returns a list with the parameter vector in the standard form, parameter matrix containing AR coefficients and component variances, mixing weights alphas, and in case of StMAR or G-StMAR model also degrees of freedom parameters.

Usage

reform_parameters(
  p,
  M,
  params,
  model = c("GMAR", "StMAR", "G-StMAR"),
  restricted = FALSE
)

Value

Returns a list with...

$params: parameter vector in the standard form.
$pars: corresponding parameter matrix containing AR coefficients and component variances. First row for phi0 or means depending on the parametrization. Column for each component.
$alphas: numeric vector containing mixing weight parameters for all of the components (also for the last one).
$dfs: numeric vector containing degrees of freedom parameters for all of components. Returned only if model == "StMAR" or model == "G-StMAR".

@keywords internal

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.

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 $2$.

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.

Details

This function does not support models imposing linear constraints. No argument checks in this function.