tacvfARFIMA {arfima} | R Documentation |

Calculates the tacvf of a mixed long memory-ARMA (with posible seasonal components). Combines long memory and ARMA (and non-seasonal and seasonal) parts via convolution.

tacvfARFIMA(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, maxlag, useCt = T, sigma2 = 1)

`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. |

`maxlag` |
The number of terms to compute: technically the output sequence is from lags 0 to maxlag, so there are maxlag + 1 terms. |

`useCt` |
Whether or not to use C to compute the (parts of the) tacvf. |

`sigma2` |
Used in |

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`

.

A sequence of length maxlag + 1 (lags 0 to maxlag) of the tacvf of the given process.

JQ (Justin) Veenstra and A. I. McLeod

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

P. Borwein (1995) An efficient algorithm for Riemann Zeta function Canadian Math. Soc. Conf. Proc., 27, pp. 29-34.

t1 <- tacvfARFIMA(phi = c(0.2, 0.1), theta = 0.4, dfrac = 0.3, maxlag = 30) t2 <- tacvfARFIMA(phi = c(0.2, 0.1), theta = 0.4, H = 0.8, maxlag = 30) t3 <- tacvfARFIMA(phi = c(0.2, 0.1), theta = 0.4, alpha = 0.4, maxlag = 30) plot(t1, type = "o", col = "blue", pch = 20) lines(t2, type = "o", col = "red", pch = 20) lines(t3, type = "o", col = "purple", pch = 20) #they decay at about the same rate

[Package *arfima* version 1.7-0 Index]