Description Usage Arguments Details Value Author(s)

Fit a generalized ARMA model for univariate time series. The ARMA is generalized in a way that AR and MA components can be specified in any lag orders.

1 |

`X` |
a data vector or a n by 1 matrix |

`U` |
number of data points burned-in. Upper bound for seasonality, i.e. U > max(S1,S2) |

`p` |
number of regular AR components |

`q` |
number of regular MA components |

`S1` |
a set of lag orders of additional AR components |

`S2` |
a set of lag orders of additional MA components |

`W` |
exogenous variable matrix p by n |

`crit` |
selection criterion. crit = c('BC','AIC','BIC') |

The model is estimated by BFGS algorithm in optim(). Note that in univariate ARMA estimation, quasi-Newton method usually provide a robust result rather than aggressive ML with second order algorithms.

The algorithm optimize conditional likelihood based on burned in samples. This is specified by argument U. U has to be greater than p,q or any element in seasonality terms.

For models that have diverging estimation, the aic value will be recorded as Inf.

`U` |
n-burnin |

`p` |
number of regular AR components |

`phi` |
estimated coefficients of regular AR components |

`q` |
number of regular MA components |

`psi` |
estimated coefficients of regular MA components |

`r1` |
length of S1 |

`S1` |
a set of lag orders of additional AR components |

`tau1` |
estimated coefficients of additional AR components |

`r2` |
length of S2 |

`S2` |
a set of lag orders of additional MA components |

`tau2` |
estimated coefficients of additional MA components |

`gamma` |
estimated coefficients of exogenous variables |

`sigma` |
estimated sigma of white noise |

`ic` |
information criterion |

Tianyang Xie

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