uGMAR (version 3.2.0)

reformRestrictedPars: Reform parameter vector with restricted autoregressive parameters to correspond non-restricted parameter vector.

Description

reformRestrictedPars reforms parameter vector with restricted autoregressive parameters to correspond non-restricted parameter vector.

Usage

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

Arguments

p

a positive integer specifying the order of AR coefficients.

M

For GMAR and StMAR models:

a positive integer specifying the number of mixture components.

For G-StMAR model:

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.

params

a real valued parameter vector specifying the model.

For non-restricted models:

For GMAR model:

Size $(M(p+3)-1x1)$ vector $\theta$$=$(${\upsilon }_1$,...,${\upsilon }_M$, ${\alpha }_1,...,{\alpha }_{M-1}$), where ${\upsilon }_m$$=({\varphi }_{m,0},$${\varphi }_m$$,{\sigma }_m^2)$ and ${\varphi }_m$=$({\varphi }_{m,1},...,{\varphi }_{m,p}),m=1,...,M$.

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 ($\theta ,\nu$)$=$(${\upsilon }_1$,...,${\upsilon }_M$, ${\alpha }_1,...,{\alpha }_{M-1},{\nu }_{M1+1},...,{\nu }_M$).

With linear constraints:

Replace the vectors ${\varphi }_m$ with vectors ${\psi }_m$ and provide a list of constraint matrices C that satisfy ${\varphi }_m$$=$$R_m{\psi }_m$ for all $m=1,...,M$, where ${\psi }_m$$=({\psi }_{m,1},...,{\psi }_{m,q_m})$.

For restricted models:

For GMAR model:

Size $(3M+p-1x1)$ vector $\theta$$=({\varphi }_{1,0},...,{\varphi }_{M,0},$$\varphi$$,{\sigma }_1^2,...,{\sigma }_M^2,{\alpha }_1,...,{\alpha }_{M-1})$, where $\varphi$=$({\varphi }_1,...,{\varphi }_M)$.

For StMAR model:

Size $(4M+p-1x1)$ vector ($\theta ,\nu$)$=({\varphi }_{1,0},...,{\varphi }_{M,0},$$\varphi$$,{\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 ($\theta ,\nu$)$=({\varphi }_{1,0},...,{\varphi }_{M,0},$$\varphi$$,{\sigma }_1^2,...,{\sigma }_M^2,{\alpha }_1,...,{\alpha }_{M-1},{\nu }_{M1+1},...,{\nu }_M)$.

With linear constraints:

Replace the vector $\varphi$ with vector $\psi$ and provide a constraint matrix $C$ that satisfies $\varphi$$=$$R\psi$, where $\psi$$=({\psi }_1,...,{\psi }_q)$.

Symbol $\varphi$ 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 ${\varphi }_{m,0}$ with regimewise mean ${\mu }_m={\varphi }_{m,0}/(1-\sum {\varphi }_{i,m})$. 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 $2$.

model

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.

restricted

a logical argument stating whether the AR coefficients ${\varphi }_{m,1},...,{\varphi }_{m,p}$ are restricted to be the same for all regimes.

Value

Returns such parameter vector corresponding to the input vector that is the form describted in params for non-restricted models (for non-constrained models). Linear constraints are not supported.