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.

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

`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. |

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

List containing

`..$A0` |
intercepts |

`..$A` |
AR coefficients |

`..$sigma` |
variance of innovation |

`..$prior` |
prior probabilities |

`..$transmat` |
transition matrix |

`..$par_emis` |
emission parameters |

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

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

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