Combining singular spectrum analysis and PAR(p) structures to model wind speed time series

Singular spectrum analysis (SSA) is a technique that decomposes a time series into a set of components, such as, trend, harmonics, and residuals. Leaving out the residual components and adding up the others, the time series can be smoothed. This procedure has been used to model Brazilian electricity consumption and flow series. The PAR(p), periodic autoregressive models, has been broadly used in modelling energy series in Brazil. This paper presents an approach of this decomposition method, by fitting the PAR(p), considering its multivariate version known as multivariate SSA (MSSA). The method was applied to a vector of two wind speed series recorded at two locations in the Brazilian Northeast region. The obtained results, when compared to the univariate decomposition of each series, were far superior, showing that the spatial correlation between the two series were considered by MSSA decomposition stage.

[1]  Rahim Mahmoudvand,et al.  On the separability between signal and noise in singular spectrum analysis , 2012 .

[2]  Rahim Mahmoudvand,et al.  On the Optimal Parameters for Reconstruction and Forecasting in Singular Spectrum Analysis , 2013, Commun. Stat. Simul. Comput..

[3]  A. Zhigljavsky,et al.  Analysis of time series structure , 2013 .

[4]  A. Zhigljavsky,et al.  Forecasting European industrial production with singular spectrum analysis , 2009 .

[5]  Rahim Mahmoudvand,et al.  FILTERING AND DENOISING IN LINEAR REGRESSION ANALYSIS , 2010 .

[6]  Emmanuel Sirimal Silva,et al.  ANALYSING AND FORECASTING EUROPEAN UNION ENERGY DATA , 2013 .

[7]  K. Hipel,et al.  Time series modelling of water resources and environmental systems , 1994 .

[8]  Hossein Hassani,et al.  MULTIVARIATE SINGULAR SPECTRUM ANALYSIS: A GENERAL VIEW AND NEW VECTOR FORECASTING APPROACH , 2013 .

[9]  Jianzhong Wu,et al.  PROBABILISTIC WIND POWER FORECASTING USING A SINGLE FORECAST , 2013 .

[10]  Abdol S. Soofi,et al.  Predicting inflation dynamics with singular spectrum analysis , 2013 .

[11]  Slobodan P. Simonovic,et al.  Noise reduction in chaotic hydrologic time series: facts and doubts , 2002 .

[12]  Anatoly Zhigljavsky,et al.  Forecasting UK Industrial Production with Multivariate Singular Spectrum Analysis , 2013 .

[13]  A. Jayawardena,et al.  Noise reduction and prediction of hydrometeorological time series: dynamical systems approach vs. stochastic approach , 2000 .

[14]  Jorge Machado Damázio,et al.  Geração de cenários sintéticos de energia e vazão para o planejamento da operação energética , 2006 .

[15]  M. H. Quenouille.  Approximate tests of correlation in time-series 3 , 1949, Mathematical Proceedings of the Cambridge Philosophical Society.

[16]  Hossein Hassani,et al.  Singular Spectrum Analysis: Methodology and Comparison , 2021, Journal of Data Science.

[17]  P. Grassberger,et al.  A simple noise-reduction method for real data , 1991 .

[18]  N. Golyandina,et al.  First-order SSA-errors for long time series: model examples of simple noisy signals , 2009 .

[19]  Qiang Zhang,et al.  Singular Spectrum Analysis and ARIMA Hybrid Model for Annual Runoff Forecasting , 2011 .

[20]  Arash Miranian,et al.  Day-ahead electricity price analysis and forecasting by singular spectrum analysis , 2013 .

[21]  Reinaldo Castro Souza,et al.  HYDROELECTRIC ENERGY FORECAST , 2013 .

[22]  Reinaldo Castro Souza,et al.  RESIDENTIAL ELECTRICITY CONSUMPTION FORECASTING USING A GEOMETRIC COMBINATION APPROACH , 2013 .

[23]  Rahim Mahmoudvand,et al.  Separability and window length in singular spectrum analysis , 2011 .

[24]  C. Kubrusly.  Elements of Operator Theory , 2001 .

[25]  Shie-Yui Liong,et al.  A systematic approach to noise reduction in chaotic hydrological time series , 1999 .

[26]  Anatoly Zhigljavsky,et al.  Multivariate singular spectrum analysis for forecasting revisions to real-time data , 2011 .

[27]  Dimitrios D. Thomakos,et al.  A review on singular spectrum analysis for economic and financial time series , 2010 .