Strong coupling between values at different time that exhibit properties of long range dependence, non-stationary, spiky signals cannot be processed by the conventional time series analysis. The ARFIMA model, which employs the fractional order signal processing techniques, is the generalization of the conventional integer order models — ARIMA and ARMA model. Therefore, it has much wider applications since it could capture both short-range dependence and long range dependence. For now, several software have developed functions dealing with ARFIMA processes. However, it could be a big difference, if using different numerical tools for time series analysis. Time to time, being asked about which tool is suitable for a specific application, the authors decide to carry out this survey to present recapitulative information of the available tools in the literature, in hope of benefiting researchers with different academic backgrounds. In this paper, 4 primary functions concerning simulation, fractional order difference filter, estimation and forecast are compared and evaluated respectively in the different software and informative comments are also provided for selection.
Fractional order fuzzy control of nuclear reactor power with thermal-hydraulic effects in the presence of random network induced delay and sensor noise having long range dependence