get_alpha_mt computes the mixing weights based on
the logarithm of the multivariate normal densities in the definition of
the mixing weights.
get_alpha_mt(M, log_mvdvalues, alphas, epsilon, conditional, also_l_0 = FALSE)Returns the mixing weights a matrix of the same dimension as log_mvdvalues so
that the t:th row is for the time point t and m:th column is for the regime m.
a positive integer specifying the number of mixture components.
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.
\(T x M\) matrix containing the log multivariate normal densities.
\(M x 1\) vector containing the mixing weight pa
the smallest number such that its exponent is wont classified as numerically zero
(around -698 is used).
a logical argument specifying whether the conditional or exact log-likelihood function should be used.
return also l_0 (the first term in the exact log-likelihood function)?
Note that we index the time series as \(-p+1,...,0,1,...,T\) as in Kalliovirta et al. (2016).
Kalliovirta L., Meitz M. and Saikkonen P. 2016. Gaussian mixture vector autoregression. Journal of Econometrics, 192, 485-498.
Virolainen S. (forthcoming). A statistically identified structural vector autoregression with endogenously switching volatility regime. Journal of Business & Economic Statistics.
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 Unpublished working paper, available as arXiv:2109.13648.
@keywords internal
loglikelihood_int