Estimation of a VMA(q) model using the exact likelihood method. Multivariate Gaussian likelihood function is used.

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`da` |
Data matrix (T-by-k) for a k-dimensional VMA process |

`q` |
The order of a VMA model |

`include.mean` |
A logicak switch to include the mean vector in estimation. Default is to include the mean vector. |

`coef0` |
Initial estimates of the coefficients used mainly in model refinement |

`secoef0` |
Standard errors of the initial estimates |

`fixed` |
A logical matrix to put zero parameter constraints |

`prelim` |
A logical switch for preliminary estimation |

`details` |
A logical switch to control output in estimation |

`thres` |
The threshold value for zero parameter constraints |

`data` |
The observed time series |

`MAorder` |
The VMA order |

`cnst` |
A logical switch to inlcude the mean vector |

`coef` |
Parameter estimayes |

`secoef` |
Standard errors of parameter estimates |

`residuals` |
Residual series |

`Sigma` |
Residual covariance matrix |

`Theta` |
VMA coefficient matrix |

`mu` |
The mean vector |

`aic,bic` |
The information criteria of the fitted model |

Ruey S. Tsay

Tsay (2014). Multivariate Time Series Analysis with R and Financial Applications. John Wiley. Hoboken, NJ.

VMA

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