Fractional Autoregressive Integrated Moving Average with Stable Innovations Model of Great Salt Lake Elevation Time Series

Chapter 8 presents an application example of fractional-order signal processing techniques in hydrology. The fractional-order signal processing techniques presented in Chap. 5 are used to study the north part of Great Salt Lake water-surface elevation time series, which possess long-range dependence and infinite variance properties. In this application example we show that FARIMA with stable innovations model can successfully characterize the Great Salt Lake historical water levels and predict its future rise and fall with much better accuracy. Therefore, we can observe that fractional-order signal processing techniques provide more powerful tools for forecasting the Great Salt Lake elevation time series with long-range dependent and infinite variance properties.

[1]  Upmanu Lall,et al.  Nonlinear Dynamics of the Great Salt Lake: Nonparametric Short-Term Forecasting , 1996 .

[2]  Ming Li,et al.  On the Predictability of Long-Range Dependent Series , 2010 .

[3]  Ted Arnow,et al.  Hydrologic characteristics of the Great Salt Lake, Utah, 1847-1986 , 1990 .

[4]  YangQuan Chen,et al.  Modeling and Prediction of Great Salt Lake Elevation Time Series Based on ARFIMA , 2007 .

[5]  Hyun-Han Kwon,et al.  Locally weighted polynomial regression: Parameter choice and application to forecasts of the Great Salt Lake , 2006 .

[6]  B. Gnedenko,et al.  Limit Distributions for Sums of Independent Random Variables , 1955 .

[7]  Edward J. Wegman,et al.  Topics in Non-Gaussian Signal Processing , 2011 .

[8]  Christophe Tricaud,et al.  Great Salt Lake Surface Level Forecasting Using FIGARCH Model , 2007 .

[9]  G. E. Ellis,et al.  Statistical Characteristics of Ocean Acoustic Noise Processes , 1989 .

[10]  Piotr Kokoszka,et al.  Fractional ARIMA with stable innovations , 1995 .

[11]  Gwilym M. Jenkins,et al.  Time series analysis, forecasting and control , 1972 .

[12]  L. Donald,et al.  of the INTERIOR , 1962 .

[13]  S. Sastry,et al.  Adaptive Control: Stability, Convergence and Robustness , 1989 .

[14]  Ted Arnow.  Water-Level and Water-Quality Changes in Great Salt Lake, Utah 1843-1985 , 1984 .

[15]  Rongtao Sun.  FRACTIONAL ORDER SIGNAL PROCESSING: TECHNIQUES AND APPLICATIONS , 2007 .

[16]  Clive W. J. Granger,et al.  “Infinite Variance” and Research Strategy in Time Series Analysis , 1972 .