pick_alphas: Pick mixing weight parameters alpha_{m}, m=1,...,M
In gmvarkit: Estimate Gaussian and Student's t Mixture Vector Autoregressive Models

pick_alphas

R Documentation

Pick mixing weight parameters `\alpha_{m}, m=1,...,M`

Description

pick_alphas picks the mixing weight parameters from the given parameter vector.

Usage

pick_alphas(p, M, d, params, model = c("GMVAR", "StMVAR", "G-StMVAR"))

Arguments

`p`	a positive integer specifying the autoregressive order of the model.
`M`	For GMVAR and StMVAR models: a positive integer specifying the number of mixture components. For G-StMVAR models: a size (2x1) integer vector specifying the number of GMVAR type components `M1` in the first element and StMVAR type components `M2` in the second element. The total number of mixture components is `M=M1+M2`.
`d`	the number of time series in the system.
`params`	a real valued vector specifying the parameter values. For reduced form models: Should be size `((M(pd^2+d+d(d+1)/2+2)-M1-1)x1)` and have the form `\theta` `=` (`\upsilon``_{1}`, ...,`\upsilon``_{M}`, `\alpha_{1},...,\alpha_{M-1},``\nu``)`, where `\upsilon``_{m}` `= (\phi_{m,0},``\phi``_{m},\sigma_{m})` `\phi``_{m}` `= (vec(A_{m,1}),...,vec(A_{m,p})` and `\sigma_{m} = vech(\Omega_{m})`, m=1,...,M, `\nu``=(\nu_{M1+1},...,\nu_{M})` `M1` is the number of GMVAR type regimes. For structural model: Should have the form `\theta` `= (\phi_{1,0},...,\phi_{M,0},``\phi``_{1},...,``\phi``_{M}, vec(W),``\lambda``_{2},...,``\lambda``_{M},\alpha_{1},...,\alpha_{M-1},``\nu``)`, where `\lambda``_{m}=(\lambda_{m1},...,\lambda_{md})` contains the eigenvalues of the `m`th mixture component. Above, `\phi_{m,0}` is the intercept parameter, `A_{m,i}` denotes the `i`th coefficient matrix of the `m`th mixture component, `\Omega_{m}` denotes the error term covariance matrix of the `m`:th mixture component, and `\alpha_{m}` is the mixing weight parameter. The `W` and `\lambda_{mi}` are structural parameters replacing the error term covariance matrices (see Virolainen, 2022). If `M=1`, `\alpha_{m}` and `\lambda_{mi}` are dropped. If `parametrization=="mean"`, just replace each `\phi_{m,0}` with regimewise mean `\mu_{m}`. `vec()` is vectorization operator that stacks columns of a given matrix into a vector. `vech()` stacks columns of a given matrix from the principal diagonal downwards (including elements on the diagonal) into a vector. In the GMVAR model, `M1=M` and `\nu` is dropped from the parameter vector. In the StMVAR model, `M1=0`. In the G-StMVAR model, the first `M1` regimes are GMVAR type and the rest `M2` regimes are StMVAR type. In StMVAR and G-StMVAR models, the degrees of freedom parameters in `\nu` # should be strictly larger than two. The notation is similar to the cited literature.

Value

Returns a length M vector containing the mixing weight parameters alpha_{m}, m=1,...,M, including the non-parametrized alpha_{M}.

Warning

No argument checks!

References

Kalliovirta L., Meitz M. and Saikkonen P. 2016. Gaussian mixture vector autoregression. Journal of Econometrics, 192, 485-498.
Virolainen S. 2022. Structural Gaussian mixture vector autoregressive model with application to the asymmetric effects of monetary policy shocks. Unpublished working paper, available as arXiv:2007.04713.
Virolainen S. 2022. Gaussian and Student's t mixture vector autoregressive model with application to the asymmetric effects of monetary policy shocks in the Euro area. Unpublished working paper, available as arXiv:2109.13648.

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gmvarkit documentation built on Nov. 15, 2023, 1:07 a.m.