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Forecasting Natural Gas Prices Using Wavelets, Time Series, and Artificial Neural Networks.

Jin J, Kim J - PLoS ONE (2015)

Bottom Line: We also emphasize the boundary problem in wavelet decomposition, and compare results that consider the boundary problem case with those that do not.The empirical results show that our suggested approach can handle the boundary problem, such that it facilitates the extraction of the appropriate forecasting results.The performance of the wavelet-hybrid approach was superior in all cases, whereas the application of detail components in the forecasting was only able to yield a small improvement in forecasting performance.

View Article: PubMed Central - PubMed

Affiliation: Department of Natural Resources and Environmental Engineering, Hanyang University, Seoul, Korea.

ABSTRACT
Following the unconventional gas revolution, the forecasting of natural gas prices has become increasingly important because the association of these prices with those of crude oil has weakened. With this as motivation, we propose some modified hybrid models in which various combinations of the wavelet approximation, detail components, autoregressive integrated moving average, generalized autoregressive conditional heteroskedasticity, and artificial neural network models are employed to predict natural gas prices. We also emphasize the boundary problem in wavelet decomposition, and compare results that consider the boundary problem case with those that do not. The empirical results show that our suggested approach can handle the boundary problem, such that it facilitates the extraction of the appropriate forecasting results. The performance of the wavelet-hybrid approach was superior in all cases, whereas the application of detail components in the forecasting was only able to yield a small improvement in forecasting performance. Therefore, forecasting with only an approximation component would be acceptable, in consideration of forecasting efficiency.

No MeSH data available.


MSEs with the number of hidden nodes.
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pone.0142064.g005: MSEs with the number of hidden nodes.

Mentions: We used the Levenberg-Marquardt back propagation method for our ANN model. For this ANN model specification, we find that the most influential element in ANN forecasting is the number of hidden nodes. The number of input factors is selected based on the information criterion (AIC) of the time series models. The number of lags for the original data and the cA3 component are determined by AIC for ARIMA specification while the number of lags for the cD1, cD2, and cD3 components is determined by AIC for GARCH specification. According to Reboredo and Rivera-Castro [38], the detail component represents the volatility of a time series. Shumway and Stoffer, and Francq and Zakoian [43, 48], suggest that the GARCH model is suitable for modeling this volatility. Therefore, the lags of the detail component are selected based on the GARCH model. The number of hidden nodes for both the original and decomposed series is selected by MSE, which is calculated from one-step ahead forecasting of the training set, because of its general use for checking the performance of the model [49]. Fig 5 demonstrates the MSE behavior when the number of hidden nodes changes in the original gas price series As seen in Fig 5, the use of one and two hidden node was found to be the best and the second best. However, these nodes did not satisfy the condition of training which means model was not converged. We repeatedly ran our model varying the epochs and performance goal but those models could not be converged even in the condition of over three thousand epochs and 10−9 performance goal. On the other hand, the model with three nodes was converged at one thousand epochs and 10−10 performance goal. Since an excessive number of training epochs could lead inappropriate estimation [50] and our goal is to validate the usefulness of the wavelet decomposition for the linear (ARIMA, GARCH) and non-linear (ANN) forecasting models, we selected the three nodes model as the optimal ANN model. In this way, the optimal number of hidden nodes for each component was determined. The optimal numbers of hidden nodes for the other components are listed in the Table A in S1 File.


Forecasting Natural Gas Prices Using Wavelets, Time Series, and Artificial Neural Networks.

Jin J, Kim J - PLoS ONE (2015)

MSEs with the number of hidden nodes.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4635006&req=5

pone.0142064.g005: MSEs with the number of hidden nodes.
Mentions: We used the Levenberg-Marquardt back propagation method for our ANN model. For this ANN model specification, we find that the most influential element in ANN forecasting is the number of hidden nodes. The number of input factors is selected based on the information criterion (AIC) of the time series models. The number of lags for the original data and the cA3 component are determined by AIC for ARIMA specification while the number of lags for the cD1, cD2, and cD3 components is determined by AIC for GARCH specification. According to Reboredo and Rivera-Castro [38], the detail component represents the volatility of a time series. Shumway and Stoffer, and Francq and Zakoian [43, 48], suggest that the GARCH model is suitable for modeling this volatility. Therefore, the lags of the detail component are selected based on the GARCH model. The number of hidden nodes for both the original and decomposed series is selected by MSE, which is calculated from one-step ahead forecasting of the training set, because of its general use for checking the performance of the model [49]. Fig 5 demonstrates the MSE behavior when the number of hidden nodes changes in the original gas price series As seen in Fig 5, the use of one and two hidden node was found to be the best and the second best. However, these nodes did not satisfy the condition of training which means model was not converged. We repeatedly ran our model varying the epochs and performance goal but those models could not be converged even in the condition of over three thousand epochs and 10−9 performance goal. On the other hand, the model with three nodes was converged at one thousand epochs and 10−10 performance goal. Since an excessive number of training epochs could lead inappropriate estimation [50] and our goal is to validate the usefulness of the wavelet decomposition for the linear (ARIMA, GARCH) and non-linear (ANN) forecasting models, we selected the three nodes model as the optimal ANN model. In this way, the optimal number of hidden nodes for each component was determined. The optimal numbers of hidden nodes for the other components are listed in the Table A in S1 File.

Bottom Line: We also emphasize the boundary problem in wavelet decomposition, and compare results that consider the boundary problem case with those that do not.The empirical results show that our suggested approach can handle the boundary problem, such that it facilitates the extraction of the appropriate forecasting results.The performance of the wavelet-hybrid approach was superior in all cases, whereas the application of detail components in the forecasting was only able to yield a small improvement in forecasting performance.

View Article: PubMed Central - PubMed

Affiliation: Department of Natural Resources and Environmental Engineering, Hanyang University, Seoul, Korea.

ABSTRACT
Following the unconventional gas revolution, the forecasting of natural gas prices has become increasingly important because the association of these prices with those of crude oil has weakened. With this as motivation, we propose some modified hybrid models in which various combinations of the wavelet approximation, detail components, autoregressive integrated moving average, generalized autoregressive conditional heteroskedasticity, and artificial neural network models are employed to predict natural gas prices. We also emphasize the boundary problem in wavelet decomposition, and compare results that consider the boundary problem case with those that do not. The empirical results show that our suggested approach can handle the boundary problem, such that it facilitates the extraction of the appropriate forecasting results. The performance of the wavelet-hybrid approach was superior in all cases, whereas the application of detail components in the forecasting was only able to yield a small improvement in forecasting performance. Therefore, forecasting with only an approximation component would be acceptable, in consideration of forecasting efficiency.

No MeSH data available.