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

Description

The M step contains two parts. One for the estimation of the parameters of the hidden Markov chain and the other for the parameters of the auto-regressive models. A numerical algortihm is used for the emission parameters.

Usage

1
Mstep.hn.MSAR(data, theta, FB, covar = NULL, verbose = FALSE)

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

emissions covariates (the covariables act on the intercepts)

verbose

if verbose is TRUE some iterations of the numerical optimisation are print on the console.

Details

The default numerical optimization method is ucminf (see ucminf).

Value

List containing

..$A0

intercepts

..$A

AR coefficients

..$sigma

variance of innovation

..$prior

prior probabilities

..$transmat

transition matrix

..$par_emis

emission 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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