M step of the EM algorithm for fitting homogeneous multivariate Markov switching auto-regressive models with penalization of parameters of the VAR(1) models, called in fit.MSAR. Penalized maximum likelihood is used. Penalization may be add to the autoregressive matrices of order 1 and to the precision matrices (inverse of variance of innovation).
Usage
Mstep.hh.lasso.MSAR(data, theta, FB)
Arguments
data
array of univariate or multivariate series with dimension T x N.samples x d.
T: number of time steps of each sample, N.samples: number of realisations of the same stationary process, d: dimension.
theta
model's parameter; object of class MSAR. See also init.theta.MSAR.
FB
Forward-Backward results, obtained by calling Estep.MSAR function
Value
A0
intercepts
A
AR coefficients
sigma
variance of innovation
sigma.inv
inverse of variance of innovation
prior
prior probabilities
transmat
transition matrix
Details
The lars algorithm of pagkage lars is used.
References
Efron, B., Hastie, T., Johnstone, I., Tibshirani, R., et al. (2004). Least angle regression. The Annals of statistics, 32(2):407-499.