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). Ridge, LASSO and SCAD penalization are implmented for the autoregressive matrices and only SCAD for the precision matrices.
Mstep.hh.SCAD.MSAR(data, theta, FB, lambda1=.1,lambda2=.1,penalty=,par=NULL)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.
model's parameter; object of class MSAR. See also init.theta.MSAR.
Forward-Backward results, obtained by calling Estep.MSAR function
penalization constant for the precision matrices. It may be a scalar or a vector of length M (with M the number of regimes). If it is equal to0 no penalization is introduced for the precision matrices.
penalization constant for the autoregressive matrices. It may be a scalar or a vector of length M (with M the number of regimes). If it is equal to0 no penalization is introduced for the atoregression matrices.
choice of the penalty for the autoregressive matrices. Possible values are ridge, lasso or SCAD (default).
allows to give an initial value to the precision matrices.
intercepts
AR coefficients
variance of innovation
inverse of variance of innovation
prior probabilities
transition matrix
When LASSO penalty is chosen, the LARS algorithm is used. When SCAD is chosen, a Newton-Raphson algorithm is run with a quadratic approximation of the penalized likelihood. For the precision matrices penalization, the package glasso is used.
Limit of this function: only works for VAR(1) models
Efron, B., Hastie, T., Johnstone, I., Tibshirani, R., et al. (2004). Least angle regression. The Annals of statistics, 32(2):407-499.
Fan, J. and Li, R. (2001). Variable selection via nonconcave penalized likelihood and its oracle properties. Journal of the American statistical Association, 96(456):1348-1360.
Mstep.hh.MSAR, fit.MSAR