Singular Spectrum Analysis (SSA) is a non-parametric technique that allows the decomposition of a time series into signal and noise. Thus, it is a useful technique to trend extraction, smooth and filter a time series. The effect on performance of both Box and Jenkins' and Holt-Winters models when applied to the time series filtered by SSA is investigated in this paper. Three different methodologies are evaluated in the SSA approach: Principal Component Analysis (PCA), Cluster Analysis and Graphical Analysis of Singular Vectors. In order to illustrate and compare the methodologies, in this paper, we also present the main results of a computational experiment with the monthly residential consumption of electricity in Brazil.
ABSTRACT. This paper proposes a method (denoted by WD-ANN) that combines the Artificial Neural Networks (ANN) and the Wavelet Decomposition (WD) to generate short-term global horizontal solar radiation forecasting, which is an essential information for evaluating the electrical power generated from the conversion of solar energy into electrical energy. The WD-ANN method consists of two basic steps: firstly, it is performed the decomposition of level p of the time series of interest, generating p + 1 wavelet orthonormal components; secondly, the p + 1 wavelet orthonormal components (generated in the step 1) are inserted simultaneously into an ANN in order to generate short-term forecasting. The results showed that the proposed method (WD-ANN) improved substantially the performance over the (traditional) ANN method.
ResumoSingular Spectrum Analysis (SSA) é uma técnica não-paramétrica que permite decompor uma série temporal em sinal e ruído. Neste artigo, os modelos Box & Jenkins e Holt-Winters são testados com e sem a abordagem SSA para a modelagem de uma série temporal de consumo residencial mensal de energia elétrica de uma concessionária do Rio de Janeiro. Três diferentes metodologias são utilizadas na abordagem SSA: Análise de Componentes principais (ACP), ACP associado com Análise de Cluster e Análise Gráfica dos Vetores Singulares. MAPE, MAE, RMSE e R 2 são estatísticas usadas para testar o poder preditivo dos modelos. Os resultados mostram um maior poder preditivo do modelo quando aplicado a séries filtradas em conjunto com a técnica SSA. Palavras Chave: SSA, ARIMA, Holt-Winters, consumo de energia.
AbstractSingular Spectrum Analysis (SSA) is a non-parametric technique to decompose a time series into signal and noise. In this article, the Box-Jenkins and Holt-Winters models are tested with and without SSA approach for modeling a time series of monthly residential electricity consumption from a dealership in Rio de Janeiro. Three different methodologies are used in the SSA approach: Analysis of Main Components (ACP), ACP associated with Cluster Analysis and Graphical Analysis of Singular Vectors. MAPE, MAE, RMSE and R2 statistics are used to test the predictive power of the models. The results show a greater predictive power of the model when applied in conjunction with the filtered technique SSA series.
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