This paper proposed a methodology that integrates the
Box & Jenkins modeling, the Wavelet Decomp... more This paper proposed a methodology that integrates the Box & Jenkins modeling, the Wavelet Decomposition and the Mathematical Programming in time series forecasting. Initially, the time series is decomposed into wavelet components. Then, each wavelet component is modeled through the Box & Jenkins’ approach, and forecasts are generated for each component. Finally, the predictions of each wavelet component are linearly combined using a mathematical programming model in order to predict the time series.
International Journal of Energy and Statistics, Jun 2013
The forecasting of electricity consumption and demand plays a pivotal role in electric power syst... more The forecasting of electricity consumption and demand plays a pivotal role in electric power systems planning. This paper proposes the combination of forecasts from two approaches with the aim of improving the forecasting accuracy, in order to make the best use of the installed transmission and generating capacity. In the first approach, the consumption time series is decomposed by wavelet analysis and a Box-Jenkins model is fitted to each wavelet component, following which the individual components forecasts are added to compute the total consumption forecast. The alternative approach, uses the Singular Spectrum Analysis technique to model the consumption time series in order to shrink the noise level. Thereafter, the Box-Jenkins model is used to forecast the filtered time series, producing a second forecast for the consumption series. Eventually, the two forecasts are combined geometrically in order to minimize the mean square error. The proposed methodology is illustrated by a computational experiment with the time series of residential consumption of electricity in Brazil.
XVIII Simpósio de Pesquisa Operacional e Logística da Marinha SPOLM, Jul 6, 2015
Singular spectrum analysis (SSA) is a technique that decomposes a time series into a set of compo... more 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. The scenarios generations through PAR(p), periodic autoregressive models, has been broadly used in modeling Affluent natural Energy series. This article presents an approach of this decomposition method, in which the PAR (p) model is applied to the smoothed series obtained by SSA and its multivariate version, named MSSA. In this case, 200 scenarios are generated for a forecasting horizon of 60 months. To illustrate the application of the proposed methodology were considered wind speed time series recorded at two locations in northeastern Brazil. The results show that both the PAR (p) model and scenarios generations are favored by prior smoothing of the time series by SSA / MSSA.
XVIII Simpósio de Pesquisa Operacional e Logística da Marinha SPOLM, Jul 6, 2015
The aim of this paper is to present different methods to remove noise from time series using the ... more The aim of this paper is to present different methods to remove noise from time series using the Singular Spectrum Analysis (SSA) and verify performance of Density Based Spatial Clustering of Applications with Noise (DBSCAN) before others. For this purpose, four approaches were used in the grouping step of the method SSA: Principal Component Analysis (PCA), Clustering Analysis integrated with PCA, Graphical Analysis of Singular Eigenvectors and DBSCAN. In addition, statistical tests were performed in order to empirically demonstrate statistical independence and second-order stationarity in the time series of noise removed. To illustrate the application of methods, we considered the time series of flow of the Governor Bento Munhoz Hydroelectric Plant, located on the Paraná River Basin.
XVI Simpósio de Pesquisa Operacional e Logística da Marinha, Aug 15, 2013
In this paper, we compare four forecasting methods: Box and Jenkins (BJ); Box and Jenkins
with W... more In this paper, we compare four forecasting methods: Box and Jenkins (BJ); Box and Jenkins
with Wavelet Theory (BJ-WT); Box and Jenkins with Singular Spectrum Analysis (BJ-SSA);
and Geometric Combination of BJ-WT and BJ-SSA methods. The methods were applied to
the time series of monthly residential consumption of electricity in a part of the State of Rio
de Janeiro, Brazil. The results show that the Geometric Combination of BJ-WT and BJ-SSA
methods significantly improved the performance over all other methods.
XVI Simpósio de Pesquisa Operacional e Logística da Marinha, Aug 15, 2013
The Periodic Autoregressive Model Family Box & Jenkins - PAR(p) has been employed in the predicti... more The Periodic Autoregressive Model Family Box & Jenkins - PAR(p) has been employed in the prediction of Affluent Natural Energy (ENA), an important variable in the energetic operation planning of hydroelectric systems. In order to increase the accuracy of the ENA’s predictions obtained by the PAR(p) model, we propose the application of Multi-Channel Singular Spectrum Analysis - MSSA in the simultaneous filtering of the ENA series of the four subsystems that comprise the National Interconnected System. The PAR(p) models are adjusted to the filtered time series and the resulting predictions are compared with those obtained by models PAR(p) adjusted to the original time series. The results presented in the paper show the effectiveness of filtering in improving the accuracy of ENA’s predictions obtained by the PAR(p) model.
Singular Spectrum Analysis (SSA) is a non-parametric technique that allows the decomposition of a... more 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.
This paper proposes a method (denoted by WD-ANN) that combines the Artificial Neural Networks (AN... more 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.
International Workshop on Energy Efficiency for a More Sustainable World, Sep 2012
In this paper, we compare the performances of three forecasting methods: Artificial Neural
Netw... more In this paper, we compare the performances of three forecasting methods: Artificial Neural
Networks (ANN), Artificial Neural Networks integrated with Wavelet Decomposition (WD-ANN),
Artificial Neural Networks integrated with Singular Spectrum Analysis and Wavelet (SSA-WD-ANN).
The methods were applied to a wind speed time series from an anemometric station in Brazil. The results
show that the SSA-WT-ANN method not only significantly improved the performance over all other
methods but also could be made straightforwardly operational to generate short-term wind speed and wind
power forecasts.
To model a time series of monthly residential consumption of electricity, three different methodo... more To model a time series of monthly residential consumption of electricity, three different methodologies are used in SSA approach and the Box and Jenkins’ and Holt-Winters
models are tested with and without SSA approach. MAPE, MAD, RMSE and R2 statistics are used to testing the predictive power of models.
Singular spectrum analysis (SSA) is a technique that decomposes a time series into a
set of comp... more 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.
Singular spectrum analysis (SSA) is a technique that decomposes a time series into a set of compo... more 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. The PAR(p), periodic autoregressive models, has been broadly used in modeling Affluent natural Energy series. This article presents an approach of this decomposition method, in which the PAR (p) model is applied to the smoothed series obtained by SSA and its multivariate version, named MSSA. To illustrate the application of the proposed methodology were considered wind speed time series recorded at two locations in northeastern Brazil. The results show that the PAR (p) model is favored by prior smoothing of the time series by SSA / MSSA.
XVII Simpósio de Pesquisa Operacional & Logística da Marinha, 2014
The entry into operation of new wind farms in the National Interconnected System (NIS) points out... more The entry into operation of new wind farms in the National Interconnected System (NIS) points out to the need for developing of wind power forecasting models. This work investigates the performance of a nonparametric technique called Singular Spectrum Analysis (SSA) to predict the monthly wind power output. The implementation of SSA is illustrated by means of a wind speed time series provided by the National Organization Environmental Data System (Sonda Project). Additionally, the performance achieved by the SSA was compared with the results obtained by the parametric approach of Box & Jenkins traditionally used in modeling monthly time series.
Singular spectrum analysis (SSA) is a technique that decomposes a time series into a set of compo... more 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.
Brazilian Journal of Probability and Statistics (2006), 20, pp. 112. c Associaçao Brasileira de... more Brazilian Journal of Probability and Statistics (2006), 20, pp. 112. c Associaçao Brasileira de Estatıstica ... A non-linear eroder in presence of one-sided noise ... Moisés Lima de Menezes1 and André Toom2 1University Federal of Mato Grosso 2University Federal of Pernambuco
Singular Spectrum Analysis (SSA) is a non-parametric technique that allows the decomposition of a... more 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.
This paper proposed a methodology that integrates the
Box & Jenkins modeling, the Wavelet Decomp... more This paper proposed a methodology that integrates the Box & Jenkins modeling, the Wavelet Decomposition and the Mathematical Programming in time series forecasting. Initially, the time series is decomposed into wavelet components. Then, each wavelet component is modeled through the Box & Jenkins’ approach, and forecasts are generated for each component. Finally, the predictions of each wavelet component are linearly combined using a mathematical programming model in order to predict the time series.
International Journal of Energy and Statistics, Jun 2013
The forecasting of electricity consumption and demand plays a pivotal role in electric power syst... more The forecasting of electricity consumption and demand plays a pivotal role in electric power systems planning. This paper proposes the combination of forecasts from two approaches with the aim of improving the forecasting accuracy, in order to make the best use of the installed transmission and generating capacity. In the first approach, the consumption time series is decomposed by wavelet analysis and a Box-Jenkins model is fitted to each wavelet component, following which the individual components forecasts are added to compute the total consumption forecast. The alternative approach, uses the Singular Spectrum Analysis technique to model the consumption time series in order to shrink the noise level. Thereafter, the Box-Jenkins model is used to forecast the filtered time series, producing a second forecast for the consumption series. Eventually, the two forecasts are combined geometrically in order to minimize the mean square error. The proposed methodology is illustrated by a computational experiment with the time series of residential consumption of electricity in Brazil.
XVIII Simpósio de Pesquisa Operacional e Logística da Marinha SPOLM, Jul 6, 2015
Singular spectrum analysis (SSA) is a technique that decomposes a time series into a set of compo... more 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. The scenarios generations through PAR(p), periodic autoregressive models, has been broadly used in modeling Affluent natural Energy series. This article presents an approach of this decomposition method, in which the PAR (p) model is applied to the smoothed series obtained by SSA and its multivariate version, named MSSA. In this case, 200 scenarios are generated for a forecasting horizon of 60 months. To illustrate the application of the proposed methodology were considered wind speed time series recorded at two locations in northeastern Brazil. The results show that both the PAR (p) model and scenarios generations are favored by prior smoothing of the time series by SSA / MSSA.
XVIII Simpósio de Pesquisa Operacional e Logística da Marinha SPOLM, Jul 6, 2015
The aim of this paper is to present different methods to remove noise from time series using the ... more The aim of this paper is to present different methods to remove noise from time series using the Singular Spectrum Analysis (SSA) and verify performance of Density Based Spatial Clustering of Applications with Noise (DBSCAN) before others. For this purpose, four approaches were used in the grouping step of the method SSA: Principal Component Analysis (PCA), Clustering Analysis integrated with PCA, Graphical Analysis of Singular Eigenvectors and DBSCAN. In addition, statistical tests were performed in order to empirically demonstrate statistical independence and second-order stationarity in the time series of noise removed. To illustrate the application of methods, we considered the time series of flow of the Governor Bento Munhoz Hydroelectric Plant, located on the Paraná River Basin.
XVI Simpósio de Pesquisa Operacional e Logística da Marinha, Aug 15, 2013
In this paper, we compare four forecasting methods: Box and Jenkins (BJ); Box and Jenkins
with W... more In this paper, we compare four forecasting methods: Box and Jenkins (BJ); Box and Jenkins
with Wavelet Theory (BJ-WT); Box and Jenkins with Singular Spectrum Analysis (BJ-SSA);
and Geometric Combination of BJ-WT and BJ-SSA methods. The methods were applied to
the time series of monthly residential consumption of electricity in a part of the State of Rio
de Janeiro, Brazil. The results show that the Geometric Combination of BJ-WT and BJ-SSA
methods significantly improved the performance over all other methods.
XVI Simpósio de Pesquisa Operacional e Logística da Marinha, Aug 15, 2013
The Periodic Autoregressive Model Family Box & Jenkins - PAR(p) has been employed in the predicti... more The Periodic Autoregressive Model Family Box & Jenkins - PAR(p) has been employed in the prediction of Affluent Natural Energy (ENA), an important variable in the energetic operation planning of hydroelectric systems. In order to increase the accuracy of the ENA’s predictions obtained by the PAR(p) model, we propose the application of Multi-Channel Singular Spectrum Analysis - MSSA in the simultaneous filtering of the ENA series of the four subsystems that comprise the National Interconnected System. The PAR(p) models are adjusted to the filtered time series and the resulting predictions are compared with those obtained by models PAR(p) adjusted to the original time series. The results presented in the paper show the effectiveness of filtering in improving the accuracy of ENA’s predictions obtained by the PAR(p) model.
Singular Spectrum Analysis (SSA) is a non-parametric technique that allows the decomposition of a... more 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.
This paper proposes a method (denoted by WD-ANN) that combines the Artificial Neural Networks (AN... more 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.
International Workshop on Energy Efficiency for a More Sustainable World, Sep 2012
In this paper, we compare the performances of three forecasting methods: Artificial Neural
Netw... more In this paper, we compare the performances of three forecasting methods: Artificial Neural
Networks (ANN), Artificial Neural Networks integrated with Wavelet Decomposition (WD-ANN),
Artificial Neural Networks integrated with Singular Spectrum Analysis and Wavelet (SSA-WD-ANN).
The methods were applied to a wind speed time series from an anemometric station in Brazil. The results
show that the SSA-WT-ANN method not only significantly improved the performance over all other
methods but also could be made straightforwardly operational to generate short-term wind speed and wind
power forecasts.
To model a time series of monthly residential consumption of electricity, three different methodo... more To model a time series of monthly residential consumption of electricity, three different methodologies are used in SSA approach and the Box and Jenkins’ and Holt-Winters
models are tested with and without SSA approach. MAPE, MAD, RMSE and R2 statistics are used to testing the predictive power of models.
Singular spectrum analysis (SSA) is a technique that decomposes a time series into a
set of comp... more 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.
Singular spectrum analysis (SSA) is a technique that decomposes a time series into a set of compo... more 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. The PAR(p), periodic autoregressive models, has been broadly used in modeling Affluent natural Energy series. This article presents an approach of this decomposition method, in which the PAR (p) model is applied to the smoothed series obtained by SSA and its multivariate version, named MSSA. To illustrate the application of the proposed methodology were considered wind speed time series recorded at two locations in northeastern Brazil. The results show that the PAR (p) model is favored by prior smoothing of the time series by SSA / MSSA.
XVII Simpósio de Pesquisa Operacional & Logística da Marinha, 2014
The entry into operation of new wind farms in the National Interconnected System (NIS) points out... more The entry into operation of new wind farms in the National Interconnected System (NIS) points out to the need for developing of wind power forecasting models. This work investigates the performance of a nonparametric technique called Singular Spectrum Analysis (SSA) to predict the monthly wind power output. The implementation of SSA is illustrated by means of a wind speed time series provided by the National Organization Environmental Data System (Sonda Project). Additionally, the performance achieved by the SSA was compared with the results obtained by the parametric approach of Box & Jenkins traditionally used in modeling monthly time series.
Singular spectrum analysis (SSA) is a technique that decomposes a time series into a set of compo... more 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.
Brazilian Journal of Probability and Statistics (2006), 20, pp. 112. c Associaçao Brasileira de... more Brazilian Journal of Probability and Statistics (2006), 20, pp. 112. c Associaçao Brasileira de Estatıstica ... A non-linear eroder in presence of one-sided noise ... Moisés Lima de Menezes1 and André Toom2 1University Federal of Mato Grosso 2University Federal of Pernambuco
Singular Spectrum Analysis (SSA) is a non-parametric technique that allows the decomposition of a... more 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.
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Papers by Moises Menezes
Box & Jenkins modeling, the Wavelet Decomposition and the
Mathematical Programming in time series forecasting. Initially,
the time series is decomposed into wavelet components. Then, each wavelet component is modeled through the Box & Jenkins’ approach, and forecasts are generated for each component. Finally, the predictions of each wavelet component are linearly combined using a mathematical programming model in order to predict the time series.
with Wavelet Theory (BJ-WT); Box and Jenkins with Singular Spectrum Analysis (BJ-SSA);
and Geometric Combination of BJ-WT and BJ-SSA methods. The methods were applied to
the time series of monthly residential consumption of electricity in a part of the State of Rio
de Janeiro, Brazil. The results show that the Geometric Combination of BJ-WT and BJ-SSA
methods significantly improved the performance over all other methods.
Networks (ANN), Artificial Neural Networks integrated with Wavelet Decomposition (WD-ANN),
Artificial Neural Networks integrated with Singular Spectrum Analysis and Wavelet (SSA-WD-ANN).
The methods were applied to a wind speed time series from an anemometric station in Brazil. The results
show that the SSA-WT-ANN method not only significantly improved the performance over all other
methods but also could be made straightforwardly operational to generate short-term wind speed and wind
power forecasts.
models are tested with and without SSA approach. MAPE, MAD, RMSE and R2 statistics are used to testing the predictive power of models.
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.
Issue 190 by Moises Menezes
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.
Box & Jenkins modeling, the Wavelet Decomposition and the
Mathematical Programming in time series forecasting. Initially,
the time series is decomposed into wavelet components. Then, each wavelet component is modeled through the Box & Jenkins’ approach, and forecasts are generated for each component. Finally, the predictions of each wavelet component are linearly combined using a mathematical programming model in order to predict the time series.
with Wavelet Theory (BJ-WT); Box and Jenkins with Singular Spectrum Analysis (BJ-SSA);
and Geometric Combination of BJ-WT and BJ-SSA methods. The methods were applied to
the time series of monthly residential consumption of electricity in a part of the State of Rio
de Janeiro, Brazil. The results show that the Geometric Combination of BJ-WT and BJ-SSA
methods significantly improved the performance over all other methods.
Networks (ANN), Artificial Neural Networks integrated with Wavelet Decomposition (WD-ANN),
Artificial Neural Networks integrated with Singular Spectrum Analysis and Wavelet (SSA-WD-ANN).
The methods were applied to a wind speed time series from an anemometric station in Brazil. The results
show that the SSA-WT-ANN method not only significantly improved the performance over all other
methods but also could be made straightforwardly operational to generate short-term wind speed and wind
power forecasts.
models are tested with and without SSA approach. MAPE, MAD, RMSE and R2 statistics are used to testing the predictive power of models.
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.
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.