# M step of the EM algorithm.

### Description

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

### Usage

1 2 | ```
Mstep.nn.MSAR(data, theta, FB,
covar.trans = covar.trans, covar.emis = covar.emis, method = 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.trans` |
transitions covariates |

`covar.emis` |
emissions covariates (the covariates act on the intercepts) |

`method` |
permits to choice the optimization algorithm. default is "ucminf", other possible choices are "BFGS" or "L-BFGS-B |

### Value

`A0` |
intercepts |

`A` |
AR coefficients |

`sigma` |
variance of innovation |

`prior` |
prior probabilities |

`transmat` |
transition matrix |

`par_emis` |
emission parameters |

`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

Mstep.hh.MSAR