get_alpha_mt {uGMAR} | R Documentation |
Get mixing weights alpha_mt (this function is for internal use)
Description
get_alpha_mt
computes the mixing weights based on
the logarithm of the multivariate normal densities in the definition of
the mixing weights.
Usage
get_alpha_mt(
M,
log_mvnvalues,
alphas,
epsilon,
conditional,
to_return,
also_l_0 = FALSE
)
Arguments
M |
|
log_mvnvalues |
|
alphas |
|
epsilon |
the smallest number such that its exponent is wont classified as numerically zero
(around |
conditional |
a logical argument specifying whether the conditional or exact log-likelihood function should be used. |
to_return |
should the returned object be the log-likelihood value, mixing weights, mixing weights including
value for |
also_l_0 |
return also l_0 (the first term in the exact log-likelihood function)? |
Details
Note that we index the time series as -p+1,...,0,1,...,T
as in Kalliovirta et al. (2015).
Value
Returns the mixing weights a matrix of the same dimension as log_mvnvalues
so
that the t:th row is for the time point t and m:th column is for the regime m.
References
Galbraith, R., Galbraith, J. 1974. On the inverses of some patterned matrices arising in the theory of stationary time series. Journal of Applied Probability 11, 63-71.
Kalliovirta L. (2012) Misspecification tests based on quantile residuals. The Econometrics Journal, 15, 358-393.
Kalliovirta L., Meitz M. and Saikkonen P. 2015. Gaussian Mixture Autoregressive model for univariate time series. Journal of Time Series Analysis, 36(2), 247-266.
Meitz M., Preve D., Saikkonen P. 2023. A mixture autoregressive model based on Student's t-distribution. Communications in Statistics - Theory and Methods, 52(2), 499-515.
Virolainen S. 2022. A mixture autoregressive model based on Gaussian and Student's t-distributions. Studies in Nonlinear Dynamics & Econometrics, 26(4) 559-580.