M step of the EM algorithm.

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Description

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

Usage

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Mstep.nh.MSAR(data,theta,FB,covar=NULL,method=method,
ARfix=FALSE,reduct=FALSE,penalty=FALSE,sigma.diag=FALSE,
lambda1=lambda1,lambda2=lambda2,par = NULL)

Arguments

data

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.

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.

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.

Value

List containing

..$A0

intercepts

..$A

AR coefficients

..$sigma

variance of innovation

..$prior

prior probabilities

..$transmat

transition matrix

..$par.trans

transitions parameters

Author(s)

Valerie Monbet, valerie.monbet@univ-rennes1.fr

References

Ailliot P., Monbet V., (2012), Markov switching autoregressive models for wind time series. Environmental Modelling & Software, 30, pp 92-101.

See Also

fit.MSAR, init.theta.MSAR, Mstep.hh.MSAR

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