The Modeling and Prediction of Great Salt Lake Elevation Time Series Based on Arfima

The elevation of Great Salt Lake (GSL) has a great impact on the people of Utah. The flood of GSL in 1982 has caused a loss of millions of dollars. Therefore, it is very important to predict the GSL levels as precisely as possible. This paper points out the reason why conventional methods failed to describe adequately the rise and fall of the GSL levels – the long-range dependence (LRD) property. The LRD of GSL elevation time series is characterized by some most commonly used Hurst parameter estimation methods in this paper. Then, according to the revealed LRD, the autoregressive fractional integrated moving average (ARFIMA) model is applied to analyze the data and predict the future levels. We have shown that the prediction results has a better performance compared to the conventional ARMA models. ∗FOR SUBMISSION TO THE THIRD SYMPOSIUM ON FRACTIONAL DERIVATIVES AND THEIR APPLICATIONS (ASME FDTA2007) AT THE 6TH ASME INTERNATIONAL CONFERENCE ON MULTIBODY SYSTEMS, NONLINEAR DYNAMICS AND CONTROL AT THE ASME 2007 INTERNATIONAL DESIGN ENGINEERING TECHNICAL CONFERENCES, LAS VEGAS, NEVADA, USA, SEPTEMBER 4-7, 2007. HTTP://WWW.ASMECONFERENCES.ORG/IDETC07 †Jan. 2007. Corresponding author. Center for Self-Organizing and Intelligent Systems (CSOIS), UMC 4160, College of Engineering, Utah State University, Logan, Utah 84322-4160, USA. Tel. 1(435)797-0148; Fax: 1(435)797-3054. URL: http://www.csois.usu.edu/ NOMENCLATURE ARFIMA Autoregressive Fractional Integrated Moving Average FGN Fractional Gaussian noise FOC Fractional Order Calculus FOSP Fractional Order Signal Processing FrFT Fractional Fourier Transform GSL Great Salt Lake LRD Long-Range Dependence