# mle.arfima: Pseudo-Maximum Likelihood Estimation of ARFIMA Model In nsarfima: Methods for Fitting and Simulating Non-Stationary ARFIMA Models

## Description

Fits an ARFIMA(p,d,q) model to a time series using a pseudo-maximum likelihood estimator. For details see Beran (1995).

## Usage

 ``` 1 2 3 4 5 6 7 8 9 10 11``` ```mle.arfima( y, p = 1, q = 0, d.range = c(0, 1), start, incl.mean = TRUE, verbose = FALSE, method = c("Nelder-Mead", "BFGS", "CG", "L-BFGS-B", "SANN", "Brent"), control = list() ) ```

## Arguments

 `y` Numeric vector of the time series. `p` Autoregressive order. `q` Moving average order. `d.range` Range of allowable values for fractional differencing parameter. Smallest value must be greater than -1. `start` Named vector of length 1 + `p` + `q` containing initial fit values for the fractional differencing parameter, the AR parameters, and the MA parameters (e.g. `start = c(d=0.4, ar.1=-0.4, ma.1=0.3, ma.2=0.4)`). If missing, automatically selected. `incl.mean` Whether or not to include a mean term in the model. The default value of `TRUE` is recommended unless the true mean is known and previously subtracted. Mean is returned with standard error, which may be misleading for `d>=0.5`. `verbose` Whether to print summary of fit. `method` Method for `optim`, see `help(optim)`. `control` List of additional arguments for `optim`, see `help(optim)`.

## Value

A list containing:

 `pars` A numeric vector of parameter estimates. `std.errs` A numeric vector of standard errors on parameters. `cov.mat` Parameter covariance matrix (excluding mean). `fit.obj` `optim` fit object. `p.val` Ljung-Box p-value for fit. `residuals` Fit residuals.

## References

Beran, J. (1995). Maximum Likelihood Estimation of the Differencing Parameter for Short and Long Memory Autoregressive Integrated Moving Average Models. Journal of the Royal Statistical Society. Series B (Methodological), 57, No. 4, 659-672. doi: 10.1111/j.2517-6161.1995.tb02054.x

`mde.arfima` for minimum distance estimation.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16``` ```set.seed(1) x <- arfima.sim(1000, d=0.6, ar=c(-0.4)) fit <- mle.arfima(x, p=1, incl.mean=FALSE, verbose=TRUE) ## Fit Summary ## -------------------- ## Ljung-Box p-val: 0.263 ## sig2 d ar.1 ## est 1.09351 0.53933 -0.37582 ## err 0.05343 0.04442 0.05538 ## ## Correlation Matrix for ARFIMA Parameters ## sig2 d ar.1 ## sig2 1.0000 -0.3349 0.4027 ## d -0.3349 1.0000 -0.8318 ## ar.1 0.4027 -0.8318 1.0000 ```

### Example output

```Fit Summary
--------------------
Ljung-Box p-val:  0.263
sig2       d     ar.1
est 1.09351 0.53933 -0.37582
err 0.05343 0.04442  0.05538

Correlation Matrix for ARFIMA Parameters
sig2       d    ar.1
sig2  1.0000 -0.3349  0.4027
d    -0.3349  1.0000 -0.8318
ar.1  0.4027 -0.8318  1.0000
```

nsarfima documentation built on Aug. 6, 2020, 5:10 p.m.