Abstract
Strong coupling between values at different times that exhibit properties of long range dependence, non-stationary, spiky signals cannot be processed by the conventional time series analysis. The autoregressive fractional integral moving average (ARFIMA) model, a fractional order signal processing technique, is the generalization of the conventional integer order models—autoregressive integral moving average (ARIMA) and autoregressive moving average (ARMA) model. Therefore, it has much wider applications since it could capture both short-range dependence and long range dependence. For now, several software programs have been developed to deal with ARFIMA processes. However, it is unfortunate to see that using different numerical tools for time series analysis usually gives quite different and sometimes radically different results. Users are often puzzled about which tool is suitable for a specific application. We performed a comprehensive survey and evaluation of available ARFIMA tools in the literature in the hope of benefiting researchers with different academic backgrounds. In this paper, four aspects of ARFIMA programs concerning simulation, fractional order difference filter, estimation and forecast are compared and evaluated, respectively, in various software platforms. Our informative comments can serve as useful selection guidelines.
Highlights
Humans are obsessed about their future so much that they worry more about their future more than enjoying the present
It is hoped that informative guidelines are provided to the readers when they face the problem of selecting a numerical tool for a specific application
Many authors suggested the use of the fractionally autoregressive integrated moving average (ARIMA) model by using a fractional difference operator rather than an integer one could better take into account this phenomenon of Long-range dependence (LRD) [23]
Summary
Humans are obsessed about their future so much that they worry more about their future more than enjoying the present. Li et al examined four models for the GSL water level forecasting: ARMA, ARFIMA, autoregressive conditional heteroskedasticity (GARCH) and fractional integral autoregressive conditional heteroskedasticity (FIGARCH) They found that FIGARCH offers the best performance, indicating that conditional heteroscedasticity should be included in time series with high volatility [8]. Sheng and Chen proposed a new ARFIMA model with stable innovations to analyze the GSL data, and predicted the future levels They compared accuracy with previously published results [9]. We have evaluated techniques concerning the ARFIMA process so as to provide some guidelines when choosing appropriate methods to do the analysis With this motivation, this paper briefly introduces their usage and algorithms, evaluates the accuracy, compares the performance, and provides informative comments for selection.
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