FARIMA with stable innovations model of Great Salt Lake elevation time series

Great Salt Lake (GSL) is the largest salt lake in the western hemisphere, the fourth-largest terminal lake in the world. The elevation of GSL has critical effect on the people who live nearby and their properties. It is crucial to build an exact model of GSL elevation time series in order to predict the GSL elevation precisely. Although some models, such as ARIMA or FARIMA (fractional auto-regressive integrated moving average), GARCH (generalized auto-regressive conditional heteroskedasticity) and FIGARCH (fractional integral generalized auto-regressive conditional heteroskedasticity) have been proposed to characterize the variation of GSL elevation, which have been unsatisfactory. Therefore, it became a key point to build a more appropriate model of GSL elevation time series. In this paper a new model based on FARIMA with stable innovations is applied to analyze the data and predict the future elevation levels. From the analysis we can see that the new model can characterize GSL elevation time series more accurately. The new model will be beneficial to predict GSL elevation more precisely.

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

[2]  Gennady Samorodnitsky,et al.  Stable Processes and Related Topics , 1991 .

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

[4]  Charles W. Therrien,et al.  Probability and Random Processes for Electrical and Computer Engineers , 2011 .

[5]  Gennady Samorodnitsky,et al.  Characterization of linear and harmonizable fractional stable motions , 1992 .

[6]  Robert E. Cohenour,et al.  Great salt lake , 1968 .

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

[8]  C. L. Nikias,et al.  Signal processing with alpha-stable distributions and applications , 1995 .

[9]  Gwilym M. Jenkins,et al.  Time series analysis, forecasting and control , 1971 .

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

[11]  Richard A. Davis,et al.  Time Series: Theory and Methods , 2013 .

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

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

[14]  Demetris Koutsoyiannis,et al.  Coupling stochastic models of different timescales , 2001 .

[15]  Adam Loverro,et al.  Fractional Calculus : History , Definitions and Applications for the Engineer , 2004 .

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

[17]  H. E. Hurst,et al.  Long-Term Storage Capacity of Reservoirs , 1951 .

[18]  Makoto Maejima,et al.  Self-Similar Stable Processes with Stationary Increments , 1991 .

[19]  George E. P. Box,et al.  Time Series Analysis: Forecasting and Control , 1977 .

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

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

[22]  Jan Beran,et al.  Statistics for long-memory processes , 1994 .

[23]  T. Bollerslev,et al.  MODELING AND PRICING LONG- MEMORY IN STOCK MARKET VOLATILITY , 1996 .

[24]  E. Fama,et al.  Parameter Estimates for Symmetric Stable Distributions , 1971 .

[25]  J. McCulloch,et al.  Simple consistent estimators of stable distribution parameters , 1986 .

[26]  Hu Sheng,et al.  Robustness Analysis of the Estimators for Noisy Long-Range Dependent Time Series , 2009 .

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

[28]  K. Chung,et al.  Limit Distributions for Sums of Independent Random Variables. , 1955 .

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

[30]  M. Taqqu,et al.  Stable Non-Gaussian Random Processes : Stochastic Models with Infinite Variance , 1995 .