pick_allA picks all coefficient matrices \(A_{m,i} (i=1,..,p, m=1,..,M)\)
from the given parameter vector so that they are arranged in a 4D array with the fourth dimension
indicating each component and third dimension indicating each lag.
pick_allA(p, M, d, params)a positive integer specifying the autoregressive order of the model.
a positive integer specifying the number of mixture components.
number of time series in the system.
a real valued vector specifying the parameter values. Should be size \(((M(pd^2+d+d(d+1)/2+1)-1)x1)\) and have form \(\theta\)\( = \)(\(\upsilon\)\(_{1}\), ...,\(\upsilon\)\(_{M}\), \(\alpha_{1},...,\alpha_{M-1}\)), 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.
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.
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.
The notations are in line with the cited article by KMS (2016).
Returns a 4D array containing the coefficient matrices of the all components. Coefficient matrix
\(A_{m,i}\) can be obtained by choosing [, , i, m].
No argument checks!
Kalliovirta L., Meitz M. and Saikkonen P. 2016. Gaussian mixture vector autoregression. Journal of Econometrics, 192, 485-498.
Lutkepohl H. 2005. New Introduction to Multiple Time Series Analysis, Springer.