Singular spectrum analysis and forecasting of hydrological time series

Abstract The singular spectrum analysis (SSA) technique is applied to some hydrological univariate time series to assess its ability to uncover important information from those series, and also its forecast skill. The SSA is carried out on annual precipitation, monthly runoff, and hourly water temperature time series. Information is obtained by extracting important components or, when possible, the whole signal from the time series. The extracted components are then subject to forecast by the SSA algorithm. It is illustrated the SSA ability to extract a slowly varying component (i.e. the trend) from the precipitation time series, the trend and oscillatory components from the runoff time series, and the whole signal from the water temperature time series. The SSA was also able to accurately forecast the extracted components of these time series.

[1]  Marco Sandri,et al.  Combining Singular-Spectrum Analysis and neural networks for time series forecasting , 2005, Neural Processing Letters.

[2]  K. P. Sudheer,et al.  A neuro-fuzzy computing technique for modeling hydrological time series , 2004 .

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

[4]  Keith W. Hipel,et al.  Forecasting monthly riverflow time series , 1985 .

[5]  Francesco Masulli,et al.  Application of an ensemble technique based on singular spectrum analysis to daily rainfall forecasting , 2003, Neural Networks.

[6]  Klaus Fraedrich,et al.  Estimating the Dimensions of Weather and Climate Attractors , 1986 .

[7]  G. Kember,et al.  Forecasting river flow using nonlinear dynamics , 1993 .

[8]  Slobodan P. Simonovic,et al.  Short term streamflow forecasting using artificial neural networks , 1998 .

[9]  Witold F. Krajewski,et al.  Rainfall forecasting in space and time using a neural network , 1992 .

[10]  W. C. de Albuquerque Pereira,et al.  Performance of ultrasound echo decomposition using singular spectrum analysis. , 2001, Ultrasound in medicine & biology.

[11]  Sidney Yakowitz,et al.  A stochastic model for daily river flows in an arid region , 1973 .

[12]  Clive W. J. Granger,et al.  An introduction to long-memory time series models and fractional differencing , 2001 .

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

[14]  V. Moskvina,et al.  An Algorithm Based on Singular Spectrum Analysis for Change-Point Detection , 2003 .

[15]  Luca Ridolfi,et al.  Multivariate nonlinear prediction of river flows , 2001 .

[16]  S. Yakowitz,et al.  Nearest Neighbor Methods for Time Series, with Application to Rainfall/Runoff Prediction , 1987 .

[17]  Kuolin Hsu,et al.  Artificial Neural Network Modeling of the Rainfall‐Runoff Process , 1995 .

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

[19]  J. Elsner.  Analysis of Time Series Structure: SSA and Related Techniques , 2002 .

[20]  R. Vautard,et al.  Singular-spectrum analysis: a toolkit for short, noisy chaotic signals , 1992 .

[21]  Sidney Yakowitz,et al.  A nonparametric Markov Model for daily river flow , 1979 .

[22]  Salvatore Grimaldi,et al.  Linear Parametric Models Applied to Hydrological Series , 2004 .

[23]  Shie-Yui Liong,et al.  Rainfall and runoff forecasting with SSA-SVM approach , 2001 .

[24]  Asaad Y. Shamseldin,et al.  A nearest neighbour linear perturbation model for river flow forecasting , 1996 .

[25]  Farmer,et al.  Predicting chaotic time series. , 1987, Physical review letters.

[26]  R. Vautard,et al.  Singular spectrum analysis in nonlinear dynamics, with applications to paleoclimatic time series , 1989 .

[27]  R. Kumaresan,et al.  Data-adaptive principal component signal processing , 1980, 1980 19th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes.

[28]  M. Taqqu,et al.  Fractionally differenced ARIMA models applied to hydrologic time series: Identification, estimation, and simulation , 1997 .

[29]  M. Loutre,et al.  Spectral analysis of climate data , 1996 .

[30]  M. Ghil,et al.  Interdecadal oscillations and the warming trend in global temperature time series , 1991, Nature.

[31]  D. G. Watts,et al.  Application of Linear Random Models to Four Annual Streamflow Series , 1970 .

[32]  Michael Ghil,et al.  ADVANCED SPECTRAL METHODS FOR CLIMATIC TIME SERIES , 2002 .

[33]  W. Briggs.  Statistical Methods in the Atmospheric Sciences , 2007 .

[34]  Bellie Sivakumar,et al.  River flow forecasting: use of phase-space reconstruction and artificial neural networks approaches , 2002 .

[35]  Assessing two different climatic models and the NCEP–NCAR reanalysis data for the description of winter precipitation in the Iberian Peninsula , 2004 .