# mde.arfima: Minimum Distance 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 minimum distance estimator. For details see Mayoral (2007).

## Usage

 ``` 1 2 3 4 5 6 7 8 9 10 11 12``` ```mde.arfima( y, p = 1, q = 0, d.range = c(0, 1), start, lag.max = floor(sqrt(length(y))), 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. `lag.max` Maximum lag to use when calculating the residual autocorrelations. For details see Mayoral (2007). `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.

## Note

This method makes no assumptions on the distribution of the innovation series, and the innovation variance does not factor into the covariance matrix of parameter estimates. For this reason, it is not included in the results, but can be estimated from the residuals—see Mayoral (2007).

## References

Mayoral, L. (2007). Minimum distance estimation of stationary and non-stationary ARFIMA processes. The Econometrics Journal, 10, 124-148. doi: 10.1111/j.1368-423X.2007.00202.x

## See Also

`mle.arfima` for psuedo-maximum likelihood 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 <- mde.arfima(x, p=1, incl.mean=FALSE, verbose=TRUE) ## Fit Summary ## -------------------- ## Ljung-Box p-val: 0.276 ## d ar.1 ## est 0.55031 -0.39261 ## err 0.03145 0.03673 ## ## Correlation Matrix for ARFIMA Parameters ## d ar.1 ## d 1.0000 0.6108 ## ar.1 0.6108 1.0000 ```

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