get_varying_h: Get differences 'h' which are adjusted for overly large...

Description Usage Arguments Details Value

View source: R/numericalDifferentiation.R

Description

get_varying_h adjusts differences for overly large degrees of freedom parameters for finite difference approximation of the derivatives of the log-likelihood function. StMAR and G-StMAR models are supported.

Usage

1
get_varying_h(p, M, params, model)

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 θ=(υ_{1},...,υ_{M}, α_{1},...,α_{M-1},ν) where

  • υ_{m}=(φ_{m,0},φ_{m},σ_{m}^2)

  • φ_{m}=(φ_{m,1},...,φ_{m,p}), m=1,...,M

  • ν=(ν_{M1+1},...,ν_{M})

  • M1 is the number of GMAR type regimes.

In the GMAR model, M1=M and the parameter ν dropped. In the StMAR model, M1=0.

If the model imposes linear constraints on the autoregressive parameters: Replace the vectors φ_{m} with the vectors ψ_{m} that satisfy φ_{m}=C_{m}ψ_{m} (see the argument constraints).

For restricted models:

Size (3M+M-M1+p-1x1) vector θ=(φ_{1,0},...,φ_{M,0},φ, σ_{1}^2,...,σ_{M}^2,α_{1},...,α_{M-1},ν), where φ=(φ_{1},...,φ_{p}) contains the AR coefficients, which are common for all regimes.

If the model imposes linear constraints on the autoregressive parameters: Replace the vector φ with the vector ψ that satisfies φ= (see the argument constraints).

Symbol φ denotes an AR coefficient, σ^2 a variance, α a mixing weight, and ν a degrees of freedom parameter. If parametrization=="mean", just replace each intercept term φ_{m,0} with the regimewise mean μ_m = φ_{m,0}/(1-∑φ_{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 α are dropped, and in the case of StMAR or G-StMAR model, the degrees of freedom parameters ν 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.

Details

This function is used for approximating gradient and Hessian of a StMAR or G-StMAR model. Large degrees of freedom parameters cause significant numerical error if too small differences are used.

Value

Returns a vector with the same length as params. For other parameters than degrees of freedom parameters larger than 100, the differences will be 6e-6. For the large degrees of freedom parameters, the difference will be signif(df/1000, digits=2).


uGMAR documentation built on Jan. 24, 2022, 5:10 p.m.