reformParameters: Reform any parameter vector into standard form.

Description

reformParameters 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

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

Arguments

a positive integer specifying the autoregressive order of the model.

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:

For GMAR 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 $\phi_{m}$=$(\phi_{m,1},...,\phi_{m,p}), m=1,...,M$.
For StMAR model:: Size $(M(p+4)-1x1)$ vector ($\theta, \nu$)$=$($\upsilon_{1}$,...,$\upsilon_{M}$, $\alpha_{1},...,\alpha_{M-1}, \nu_{1},...,\nu_{M}$).
For G-StMAR model:: Size $(M(p+3)+M2-1x1)$ vector ($\theta, \nu$)$=$($\upsilon_{1}$,...,$\upsilon_{M}$, $\alpha_{1},...,\alpha_{M-1}, \nu_{M1+1},...,\nu_{M}$).

For restricted models:

For GMAR model:: Size $(3M+p-1x1)$ vector $\theta$$=(\phi_{1,0},...,\phi_{M,0},$$\phi$$, \sigma_{1}^2,...,\sigma_{M}^2,\alpha_{1},...,\alpha_{M-1})$, where $\phi$=$(\phi_{1},...,\phi_{M})$.
For StMAR model:: Size $(4M+p-1x1)$ vector ($\theta, \nu$)$=(\phi_{1,0},...,\phi_{M,0},$$\phi$$, \sigma_{1}^2,...,\sigma_{M}^2,\alpha_{1},...,\alpha_{M-1}, \nu_{1},...,\nu_{M})$.
For G-StMAR model:: Size $(3M+M2+p-1x1)$ vector ($\theta, \nu$)$=(\phi_{1,0},...,\phi_{M,0},$$\phi$$, \sigma_{1}^2,...,\sigma_{M}^2,\alpha_{1},...,\alpha_{M-1}, \nu_{M1+1},...,\nu_{M})$.

Symbol $\phi$ denotes an AR coefficient, $\sigma^2$ a variance, $\alpha$ a mixing weight, and $\nu$ a degrees of freedom parameter. 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 $2$.

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.

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".

Details

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