lARFIMA {arfima} R Documentation

## 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.

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)

`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))

```

[Package arfima version 1.7-0 Index]