# extract_regime: Extract regime from a parameter vector In uGMAR: Estimate Univariate Gaussian and Student's t Mixture Autoregressive Models

## Description

`extract_regime` extracts the specified regime from the GMAR, StMAR, or G-StMAR model parameter vector. Doesn't extract mixing weight parameter α.

## Usage

 ``` 1 2 3 4 5 6 7 8 9 10``` ```extract_regime( p, M, params, model = c("GMAR", "StMAR", "G-StMAR"), restricted = FALSE, constraints = NULL, regime, with_dfs = TRUE ) ```

## 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=Cψ (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=Cψ, 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. `regime` a positive integer in the interval [1, M] defining which regime should be extracted. `with_dfs` Should the degrees of freedom parameter (if any) be included?

## Value

Returns a numeric vector corresponding to the regime with...

For non-restricted models:
For GMAR model:

Size (p+2x1) vector (φ_{m,0},φ_{m,1},...,φ_{m,p}, σ_{m}^2).

For StMAR model:

Size (p+3x1) vector (φ_{m,0},φ_{m,1},...,φ_{m,p}, σ_{m}^2, ν_{m}).

For G-StMAR model:

Same as GMAR for GMAR type regimes and same as StMAR for StMAR type regimes.

With linear constraints:

Parameter vector as described above, but vector φ_{m} replaced with vector ψ_{m} that satisfies φ_{m}=R_{m}ψ_{m}.

For restricted models:
For GMAR model:

Size (2x1) vector (φ_{m,0}, σ_{m}^2).

For StMAR model:

Size (3x1) vector (φ_{m,0}, σ_{m}^2, ν_{m}).

For G-StMAR model:

Same as GMAR for GMAR type regimes and same as StMAR for StMAR type regimes.

With linear constraints:

Parameter vector as described above.

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