R package arfurima for fractional unit root integral (FURI) time series, ARFIMA and ARFURIMA models

This paper introduces the arfurima package for Interminable Long Memory (ILM) time series that exhibits strong hyperbolic decay Auto Correlations Function (ACF) and large spectrum at zero frequency. The package has facilities for Auto Regressive Fractional Integral Moving Average (ARFIMA) and Auto Regressive Fractional Unit Root Integral Moving Average (ARFURIMA) models of a mean of a long memory process. The mean of this LM process can be described in each ARFIMA and ARFURIMA models with fractional differencing values of 0 < d < 1 and 1 < d < 2 respectively. The arfurima.sim, furd, arfurima and arfurima.forecast are the main functions of the package. The first function simulates the fractional unit root integral series for d such that 1 < d < 2 so the simulated series has the form of ARFURIMA (p,d,q). The second function fractionally differences the Fractional Unit Root Integral (FURI) time series and returns stationary series. The third function estimates ARFIMA or ARFURIMA model while the fourth function undertakes the forecasts. Finally, daily Malaysia ringgit to United State dollar exchange rate and Malaysia average temperature data is used to illustrate the usage of the package.