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An Evaluation of ARFIMA (Autoregressive Fractional Integral Moving Average) Programs

School of Mechanical Electronic & Information Engineering, China University of Mining and Technology,Beijing, Beijing 100083, China
Mechatronics, Embedded Systems and Automation Lab, School of Engineering, University of California, Merced, CA 95343, USA
Author to whom correspondence should be addressed.
This paper is an extended version of our paper published in An evaluation of ARFIMA programs. In Proceedings of the International Design Engineering Technical Conferences & Computers & Information in Engineering Conference, Cleveland, OH, USA, 6–9 August 2017; American Society of Mechanical Engineers: New York, NY, USA, 2017; In Press.
Axioms 2017, 6(2), 16;
Received: 13 March 2017 / Revised: 3 May 2017 / Accepted: 14 June 2017 / Published: 17 June 2017
PDF [569 KB, uploaded 20 June 2017]


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. View Full-Text
Keywords: ARFIMA; long range dependence; fractional order; survey ARFIMA; long range dependence; fractional order; survey

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Liu, K.; Chen, Y.; Zhang, X. An Evaluation of ARFIMA (Autoregressive Fractional Integral Moving Average) Programs. Axioms 2017, 6, 16.

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