uGMAR (version 3.2.5)

warn_dfs: Warn about large degrees of freedom parameter values

Description

warn_dfs warns if the model contains large degrees of freedom parameter values.

Usage

warn_dfs(
  object,
  p,
  M,
  params,
  model = c("GMAR", "StMAR", "G-StMAR"),
  restricted = FALSE,
  constraints = NULL,
  warn_about = c("derivs", "errors")
)

Arguments

object

an object to be tested

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:

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 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 ${\varphi }_{m,1},...,{\varphi }_{m,p}$ are restricted to be the same for all regimes.

constraints

specifies linear constraints applied to the autoregressive parameters.

For non-restricted models:

a list of size $(px{q}_m)$ constraint matrices $C_m$ of full column rank satisfying ${\varphi }_m$$=$$C_m{\psi }_m$ for all $m=1,...,M$, where ${\varphi }_m$$=({\varphi }_{m,1},...,{\varphi }_{m,p})$ and ${\psi }_m$$=({\psi }_{m,1},...,{\psi }_{m,q_m})$.

For restricted models:

a size $(pxq)$ constraint matrix $C$ of full column rank satisfying $\varphi$$=$$C\psi$, where $\varphi$$=({\varphi }_1,...,{\varphi }_p)$ and $\psi$$={\psi }_1,...,{\psi }_q$.

Symbol $\varphi$ denotes an AR coefficient. Note that regardless of any constraints, the nominal autoregressive order is always p for all regimes. Ignore or set to NULL if applying linear constraints is not desired.

warn_about

warn about inaccurate derivatives or standard errors?

Value

Doesn't return anything but throws a warning if any degrees of freedom parameters have value larger than 100.

Details

Either provide a class 'gsmar' object or specify the model by hand.