Comparing the Simple to Complex Automatic Methods with the Ensemble Approach in Forecasting Electrical Time Series Data
Abstract
:1. Introduction
2. Materials and Methods
2.1. The ARIMA
2.2. Exponential Smoothing
2.3. Prophet
2.4. Neural Networks
2.5. Proposed Ensemble Methods
- Step 1:
- Divide the time series data into two parts, training and testing data. Let , then the training dataset is and the testing dataset is {, where is the sample size.
- Step 2:
- Model the train data using automatic models, i.e., the ARIMA, the ETS method, the DSHW method, the TBATS model, NN, and Prophet.
- Step 3:
- Calculate the forecast values up step h ahead, where, in this work, and is the time horizon for the testing data. The forecast values, are obtained by the models listed in step 2.
- Step 4:
- Assemble the models with two weighting strategies
- based on the linear relationship function, named EnL,
- based on the nonlinear relationship function, named EnNL
- Step 5:
- Calculate the forecast values using Equation (9) for the EnL method and Equation (11) for the EnNL method.
- Step 6:
- Evaluate the model based on RMSE and MAPE using Equation (12) and Equation (13), respectively.
3. Results and Discussion
3.1. Data
- Data 1:
- US Monthly Electricity Total Net Generation
- Data 2:
- Hourly Electricity Demand in Ontario
- Data 3:
- Half-Hourly Electricity Demand in England and Wales.
- Data 4:
- Half-Hourly Electricity Demand in Victoria, Australia
3.2. Experimental Results
4. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Data | Name | Frequency | Number of Observations in the Training Data | Characteristic |
---|---|---|---|---|
1 | usmelec | Monthly | 317 | Linear trend, increasing seasonal variation |
2 | ontario | Hourly | 3648 | Nonlinear trend, relative constant seasonal variation |
3 | taylor | Half-hourly | 2354 | No trend, constant seasonal variation |
4 | vic_elec | Half-hourly | 2354 | Fluctuate in level and seasonal variation |
RMSE | MAPE | |||||||
---|---|---|---|---|---|---|---|---|
Model | Data 1 | Data 2 | Data 3 | Data 4 | Data 1 | Data 2 | Data 3 | Data 4 |
ARIMA | 6.57 | 237.78 | 1010.63 | 464.98 | 2.13% | 0.96% 2 | 2.39% | 7.35% |
ETS | 6.38 | 273.51 | 481.95 | 89.21 | 2.02% | 1.29% 2 | 1.22%2 | 1.35% 2 |
DSHW | 6.63 | 253.71 | 251.33 | 40.46 | 2.16% | 1.13% 2 | 0.65% 2 | 0.67% 2 |
TBATS | 6.40 | 246.49 | 229.59 | 43.99 | 2.03% | 1.05% 2 | 0.60% 2 | 0.75% 2 |
NN | 8.37 | 158.20 | 171.36 | 35.04 | 2.92% | 0.69% 2 | 0.44% 2 | 0.61% 2 |
Prophet | 8.45 | 1118.17 | 1467.91 | 333.53 | 2.93% | 5.58% | 4.16% | 5.96% |
EnA | 6.17 | 261.69 | 359.83 | 119.79 | 1.98% 2 | 1.27% 2 | 0.95% 2 | 2.04% |
EnL | 6.04 | 157.78 | 177.46 | 29.98 | 1.94% 2 | 0.70% 2 | 0.46% 2 | 0.52% 2 |
EnNL | 5.601 | 149.17 1 | 156.55 1 | 28.42 1 | 1.89% 1,2 | 0.67% 1,2 | 0.40% 1,2 | 0.49% 1,2 |
RMSE | MAPE | |||||||
---|---|---|---|---|---|---|---|---|
Model | Data 1 | Data 2 | Data 3 | Data 4 | Data 1 | Data 2 | Data 3 | Data 4 |
ARIMA | 9.61 | 859.75 | 5767.47 | 180.96 | 2.80% | 4.85% | 14.39% | 3.32% |
ETS | 11.19 | 986.61 | 11,724.40 | 186.51 | 2.66% | 5.59% | 27.76% | 3.56% |
DSHW | 9.87 | 1141.28 | 2094.31 | 590.19 | 2.74% | 6.67% | 5.35% | 12.94% |
TBATS | 11.66 | 918.67 | 2903.67 | 103.29 | 2.73% | 5.17% | 7.14% | 2.00% 2 |
NN | 12.29 | 1160.34 | 2357.52 | 95.41 | 3.05% | 6.52% | 6.96% | 1.98% 2 |
Prophet | 16.27 | 619.86 1 | 732.69 | 146.06 | 4.08% | 3.60% 1 | 1.95% 1,2 | 2.85% |
EnA | 10.30 | 904.52 | 3488.10 | 107.37 | 2.74% | 5.16% | 8.01% | 2.22% |
EnL | 10.92 | 1138.94 | 644.24 | 228.03 | 2.75% | 6.41% | 2.03% | 4.99% |
EnNL | 4.61 1 | 1166.62 | 627.41 1 | 76.55 1 | 1.11% 1,2 | 6.56% | 2.12% | 1.54% 1,2 |
Model | MAPE | ||||||
---|---|---|---|---|---|---|---|
h = 1 | h = 2 | h = 3 | h = 4 | h = 5 | h = 6 | h = 7 | |
ARIMA | 0.50% | 0.63% | 0.44% | 0.53% | 0.85% | 1.43% | 2.37% |
ETS | 1.03% | 1.39% | 1.43% | 1.30% | 1.10% | 1.30% | 1.91% |
DSHW | 0.13% | 0.13% | 0.42% | 0.87% | 1.48% | 2.30% | 3.39% |
TBATS | 0.55% | 0.84% | 0.81% | 0.72% | 0.93% | 1.52% | 2.66% |
NN | 0.76% | 0.89% | 0.74% | 0.56% | 0.65% | 1.09% | 2.07% |
Prophet | 2.50% | 2.91% | 3.11% | 3.02% | 2.49% | 2.86% | 3.66% |
EnA | 0.87% | 1.09% | 1.02% | 0.77% | 0.93% | 1.49% | 2.45% |
EnL | 0.86% | 1.02% | 0.90% | 0.72% | 0.75% | 1.14% | 2.07% |
EnNL | 0.75% | 0.87% | 0.72% | 0.55% | 0.64% | 1.08% | 2.05% |
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Sulandari, W.; Yudhanto, Y.; Subanti, S.; Setiawan, C.D.; Hapsari, R.; Rodrigues, P.C. Comparing the Simple to Complex Automatic Methods with the Ensemble Approach in Forecasting Electrical Time Series Data. Energies 2023, 16, 7495. https://doi.org/10.3390/en16227495
Sulandari W, Yudhanto Y, Subanti S, Setiawan CD, Hapsari R, Rodrigues PC. Comparing the Simple to Complex Automatic Methods with the Ensemble Approach in Forecasting Electrical Time Series Data. Energies. 2023; 16(22):7495. https://doi.org/10.3390/en16227495
Chicago/Turabian StyleSulandari, Winita, Yudho Yudhanto, Sri Subanti, Crisma Devika Setiawan, Riskhia Hapsari, and Paulo Canas Rodrigues. 2023. "Comparing the Simple to Complex Automatic Methods with the Ensemble Approach in Forecasting Electrical Time Series Data" Energies 16, no. 22: 7495. https://doi.org/10.3390/en16227495
APA StyleSulandari, W., Yudhanto, Y., Subanti, S., Setiawan, C. D., Hapsari, R., & Rodrigues, P. C. (2023). Comparing the Simple to Complex Automatic Methods with the Ensemble Approach in Forecasting Electrical Time Series Data. Energies, 16(22), 7495. https://doi.org/10.3390/en16227495