uGMAR (version 3.2.3)

nParams: Calculate the number of parameters

Description

nParams calculates the number of parameters that should be in the parameter vector.

Usage

nParams(
  p,
  M,
  model = c("GMAR", "StMAR", "G-StMAR"),
  restricted = FALSE,
  constraints = 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 ${\varphi }_{m,1},...,{\varphi }_{m,p}$ 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.

Value

Returns the number of parameters.