M step of the EM algorithm for fitting Markov switching auto-regressive models with non homogeneous transitions.
Mstep.nh.MSAR(data,theta,FB,covar=NULL,method=method,
ARfix=FALSE,reduct=FALSE,penalty=FALSE,sigma.diag=FALSE,sigma.equal=FALSE,
lambda1=lambda1,lambda2=lambda2,par = NULL)array of univariate or multivariate series with dimension T*N.samples*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
transitions covariates
permits to choice the optimization algorithm. default is "ucminf", other possible choices are "BFGS" or "L-BFGS-B"
if TRUE the innovation covariance matrices are diagonal.
If sigma.equal==TRUE the estimated covariance of the innovation will be the same in all regimes - available only for models with homogeneous emission probabilities (default is FALSE)
if TRUE, autoregressive matrices and innovation covariance matrices are constrained to have the same pattern (zero and non zero coefficients) as the one of initial matrices.
if TRUE the AR parameters are not estimated, they stay fixed at their initial value.
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.
List containing
intercepts
AR coefficients
variance of innovation
prior probabilities
transition matrix
transitions parameters
Ailliot P., Monbet V., (2012), Markov switching autoregressive models for wind time series. Environmental Modelling & Software, 30, pp 92-101.
fit.MSAR, init.theta.MSAR, Mstep.hh.MSAR