standard_errors: Calculate standard errors for estimates of a GMAR, StMAR, or...

Description Usage Arguments Value

View source: R/standardErrors.R

Description

standard_errors numerically approximates standard errors for the given estimates of GMAR, StMAR, or GStMAR model.

Usage

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standard_errors(
  data,
  p,
  M,
  params,
  model = c("GMAR", "StMAR", "G-StMAR"),
  restricted = FALSE,
  constraints = NULL,
  conditional = TRUE,
  parametrization = c("intercept", "mean"),
  custom_h = NULL,
  minval
)

Arguments

data

a numeric vector or class 'ts' object containing the data. NA values are not supported.

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.

restricted

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

constraints

specifies linear constraints imposed to each regime's autoregressive parameters separately.

For non-restricted models:

a list of size (pxq_{m}) constraint matrices C_{m} of full column rank satisfying φ_{m}=C_{m}ψ_{m} for all m=1,...,M, where φ_{m}=(φ_{m,1},...,φ_{m,p}) and ψ_{m}=(ψ_{m,1},...,ψ_{m,q_{m}}).

For restricted models:

a size (pxq) constraint matrix C of full column rank satisfying φ=, where φ=(φ_{1},...,φ_{p}) and ψ=ψ_{1},...,ψ_{q}.

The symbol φ denotes an AR coefficient. Note that regardless of any constraints, the autoregressive order is always p for all regimes. Ignore or set to NULL if applying linear constraints is not desired.

conditional

a logical argument specifying whether the conditional or exact log-likelihood function should be used.

parametrization

is the model parametrized with the "intercepts" φ_{m,0} or "means" μ_{m} = φ_{m,0}/(1-∑φ_{i,m})?

custom_h

a numeric vector with the same length as params specifying the difference 'h' used in finite difference approximation for each parameter separately. If NULL (default), then the difference used for differentiating overly large degrees of freedom parameters is adjusted to avoid numerical problems, and the difference is 6e-6 for the other parameters.

minval

this will be returned when the parameter vector is outside the parameter space and boundaries==TRUE.

Value

Returns approximate standard errors of the parameter values in a numeric vector.


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