Mstep.nh.MSAR: M step of the EM algorithm.
In NHMSAR: Non-Homogeneous Markov Switching Autoregressive Models

Description Usage Arguments Value Author(s) References See Also

M step of the EM algorithm for fitting Markov switching auto-regressive models with non homogeneous transitions.

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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)

`data`	array of univariate or multivariate series with dimension TN.samplesd. 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
`covar`	transitions covariates
`method`	permits to choice the optimization algorithm. default is "ucminf", other possible choices are "BFGS" or "L-BFGS-B"
`sigma.diag`	if TRUE the innovation covariance matrices are diagonal.
`sigma.equal`	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)
`reduct`	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.
`ARfix`	if TRUE the AR parameters are not estimated, they stay fixed at their initial value.
`lambda1`	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.
`lambda2`	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.
`penalty`	choice of the penalty for the autoregressive matrices. Possible values are ridge, lasso or SCAD (default).
`par`	allows to give an initial value to the precision matrices.

List containing

`..$A0`	intercepts
`..$A`	AR coefficients
`..$sigma`	variance of innovation
`..$prior`	prior probabilities
`..$transmat`	transition matrix
`..$par.trans`	transitions parameters