lARFIMA {arfima}

Exact log-likelihood of a long memory model

Description

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

Usage

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
)

Arguments

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 arima.

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 arima.

dfs

The seasonal fractional differencing parameter.

H

The Hurst parameter for fractional Gaussian noise (FGN). Should not be mixed with dfrac or alpha: see "Details".

Hs

The Hurst parameter for seasonal fractional Gaussian noise (FGN). Should not be mixed with dfs or alphas: see "Details".

alpha

The decay parameter for power-law autocovariance (PLA) noise. Should not be mixed with dfrac or H: see "Details".

alphas

The decay parameter for seasonal power-law autocovariance (PLA) noise. Should not be mixed with dfs or Hs: see "Details".

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".

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.

Value

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

Author(s)

Justin Veenstra

References

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)

See Also

arfima

lARFIMAwTF

tacvfARFIMA

Examples

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