lARFIMA {arfima} | R Documentation |

Computes the exact log-likelihood of a long memory model with respect to a given time series.

lARFIMA(z, phi = numeric(0), theta = numeric(0), dfrac = numeric(0), phiseas = numeric(0), thetaseas = numeric(0), dfs = numeric(0), H = numeric(0), Hs = numeric(0), alpha = numeric(0), alphas = numeric(0), period = 0, useC = 3)

`z` |
A vector or (univariate) time series object, assumed to be (weakly) stationary. |

`phi` |
The autoregressive parameters in vector form. |

`theta` |
The moving average parameters in vector form. See Details for
differences from |

`dfrac` |
The fractional differencing parameter. |

`phiseas` |
The seasonal autoregressive parameters in vector form. |

`thetaseas` |
The seasonal moving average parameters in vector form. See
Details for differences from |

`dfs` |
The seasonal fractional differencing parameter. |

`H` |
The Hurst parameter for fractional Gaussian noise (FGN). Should
not be mixed with |

`Hs` |
The Hurst parameter for seasonal fractional Gaussian noise (FGN).
Should not be mixed with |

`alpha` |
The decay parameter for power-law autocovariance (PLA) noise.
Should not be mixed with |

`alphas` |
The decay parameter for seasonal power-law autocovariance
(PLA) noise. Should not be mixed with |

`period` |
The periodicity of the seasonal components. Must be >= 2. |

`useC` |
How much interfaced C code to use: an integer between 0 and 3. The value 3 is strongly recommended. See "Details". |

The log-likelihood is computed for the given series z and the parameters.
If two or more of `dfrac`

, `H`

or `alpha`

are present and/or
two or more of `dfs`

, `Hs`

or `alphas`

are present, an error
will be thrown, as otherwise there is redundancy in the model. Note that
non-seasonal and seasonal components can be of different types: for example,
there can be seasonal FGN with FDWN at the non-seasonal level.

The moving average parameters are in the Box-Jenkins convention: they are
the negative of the parameters given by `arima`

.

For the useC parameter, a "0" means no C is used; a "1" means C is only used to compute the log-likelihood, but not the theoretical autocovariance function (tacvf); a "2" means that C is used to compute the tacvf and not the log-likelihood; and a "3" means C is used to compute everything.

Note that the time series is assumed to be stationary: this function does not do any differencing.

The exact log-likelihood of the model given with respect to z, up to an additive constant.

Justin Veenstra

Box, G. E. P., Jenkins, G. M., and Reinsel, G. C. (2008) Time Series Analysis: Forecasting and Control. 4th Edition. John Wiley and Sons, Inc., New Jersey.

Veenstra, J.Q. Persistence and Antipersistence: Theory and Software (PhD Thesis)

set.seed(3452) sim <- arfima.sim(1000, model = list(phi = c(0.3, -0.1))) lARFIMA(sim, phi = c(0.3, -0.1))

[Package *arfima* version 1.7-0 Index]