# A Multi-Stage Price Forecasting Model for Day-Ahead Electricity Markets

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## Abstract

**:**

## 1. Introduction

## 2. Modelling of Electricity Price & Forecasting Methods

#### 2.1. ARIMA

#### 2.2. Locally Weighted Scatterplot Smoothing (LOWESS)

#### 2.3. Support Vector Machines (SVM)

#### 2.4. Random Forest (RF)

#### 2.5. Generalized Linear Model (GLM)

## 3. Proposed Hybrid 2-Stage Model

#### 3.1. Stage-1: Initial Price Forecast (F) Using ARIMA

#### 3.2. Stage-1: Input Residuals to the Hybrid Model

#### 3.2.1. ARIMA-SVM

#### 3.2.2. ARIMA-RF

#### 3.2.3. ARIMA-LOWESS

#### 3.2.4. ARIMA-ARIMA

## 4. Explanatory (Input) Variables for Day-Ahead Price Forecast

#### Data Explanation

- (a)
- Hourly electricity price for day D and day D-6.
- (b)
- Hourly load data, including total load demand, hydro power demand, solar power demand, coal power demand, wind power demand and combined cycle power demand for day D and day D-6.
- (c)
- Hourly weather data, including temperature, wind speed and solar irradiance.

## 5. Results and Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Fan, G.F.; Peng, L.L.; Hong, W.C.; Sun, F. Electric load forecasting by the SVR model with differential empirical mode decomposition and auto regression. Neurocomputing
**2016**, 173, 958–970. [Google Scholar] [CrossRef] - Ju, F.Y.; Hong, W.C. Application of seasonal SVR with chaotic gravitational search algorithm in electricity forecasting. Appl. Math. Model.
**2013**, 37, 9643–9651. [Google Scholar] [CrossRef] - Weron, R. Electricity price forecasting: A review of the state-of-the-art with a look into the future. Int. J. Forecast.
**2014**, 30, 1030–1081. [Google Scholar] [CrossRef] - Hussain, A.; Rahman, M.; Memon, J.A. Forecasting electricity consumption in Pakistan: The way forward. Energy Policy
**2016**, 90, 73–80. [Google Scholar] [CrossRef] - Pappas, S.S.; Ekonomou, L.; Karampelas, P.; Karamousantas, D.C.; Katsikas, S.K.; Chatzarakis, G.E.; Skafidas, P.D. Electricity demand load forecasting of the Hellenic power system using an ARMA model. Electr. Power Syst. Res.
**2010**, 80, 256–264. [Google Scholar] [CrossRef] - Vu, D.H.; Muttaqi, K.M.; Agalgaonkar, A.P. A variance inflation factor and backward elimination based robust regression model for forecasting monthly electricity demand using climatic variables. Appl. Energy
**2015**, 140, 385–394. [Google Scholar] [CrossRef][Green Version] - Dudek, G. Pattern-based local linear regression models for short-term load forecasting. Electr. Power Syst. Res.
**2016**, 130, 139–147. [Google Scholar] [CrossRef] - Maçaira, P.M.; Souza, R.C.; Cyrino Oliveira, F.L. Modelling and forecasting the residential electricity consumption in Brazil with pegels exponential smoothing techniques. Procedia Comput. Sci.
**2015**, 55, 328–335. [Google Scholar] [CrossRef] - Al-Hamadi, H.M.; Soliman, S.A. Short-term electric load forecasting based on Kalman filtering algorithm with moving window weather and load model. Electr. Power Syst. Res.
**2004**, 68, 47–59. [Google Scholar] [CrossRef] - Hippert, H.S.; Taylor, J.W. An evaluation of Bayesian techniques for controlling model complexity and selecting inputs in a neural network for short-term load forecasting. Neural Netw.
**2010**, 23, 386–395. [Google Scholar] [CrossRef] [PubMed] - Zhang, W.; Yang, J. Forecasting natural gas consumption in China by bayesian model averaging. Energy Rep.
**2015**, 1, 216–220. [Google Scholar] [CrossRef] - Li, H.; Guo, S.; Li, C.; Sun, J. A hybrid annual power load forecasting model based on generalized regression neural network with fruit fly optimization algorithm. Knowl. Based Syst.
**2013**, 37, 378–387. [Google Scholar] [CrossRef] - Ertugrul, Ö.F. Forecasting electricity load by a novel recurrent extreme learning machines approach. Int. J. Electr. Power Energy Syst.
**2016**, 78, 429–435. [Google Scholar] [CrossRef] - Bennett, C.J. Forecasting low voltage distribution network demand profiles using a pattern recognition based expert system. Energy
**2014**, 67, 200–212. [Google Scholar] [CrossRef][Green Version] - Lahouar, A.; Ben Hadj Slama, J. Day-ahead load forecast using random forest and expert input selection. Energy Convers. Manag.
**2015**, 103, 1040–1051. [Google Scholar] [CrossRef] - Akdemir, B.; Çetinkaya, N. Long-term load forecasting based on adaptive neural fuzzy inference system using real energy data. Energy Procedia
**2012**, 14, 794–799. [Google Scholar] [CrossRef] - Chaturvedi, D.K.; Sinha, A.P.; Malik, O.P. Short term load forecast using fuzzy logic and wavelet transform integrated generalized neural network. Int. J. Electr. Power Energy Syst.
**2015**, 67, 230–237. [Google Scholar] [CrossRef] - Dong, Y.; Zhang, Z.; Hong, W.-C. A Hybrid Seasonal Mechanism with a Chaotic Cuckoo Search Algorithm with a Support Vector Regression Model for Electric Load Forecasting. Energies
**2018**, 11, 1009. [Google Scholar] [CrossRef] - Fan, S.; Mao, C.; Chen, L. Next-day electricity-price forecasting using a hybrid network. IET Gener. Transm. Distrib.
**2007**, 1, 176–182. [Google Scholar] [CrossRef] - Puspaningrum, A.; Sarno, R. A hybrid cuckoo optimization and harmony search algorithm for software cost estimation. Procedia Comput. Sci.
**2017**, 124, 461–469. [Google Scholar] [CrossRef] - Huang, L.; Ding, S.; Yu, S.; Wang, J.; Lu, K. Chaos-enhanced cuckoo search optimization algorithms for global optimization. Appl. Math. Model.
**2016**, 40, 3860–3875. [Google Scholar] [CrossRef] - Wu, L.; Shahidehpour, M. A hybrid model for day-ahead price forecasting. IEEE Trans. Power Syst.
**2010**, 25, 1519–1530. [Google Scholar] - Wu, L.; Shahidehpour, M. A hybrid model for integrated day-ahead electricity price and load forecasting in smart grid. IET Gener. Transm. Distrib.
**2014**, 8, 1937–1950. [Google Scholar] [CrossRef] - Jónsson, T.; Pinson, P.; Nielsen, H.A.; Madsen, H.; Nielsen, T.S. Forecasting electricity spot prices accounting for wind power predictions. IEEE Trans. Sustain. Energy
**2013**, 4, 210–218. [Google Scholar] [CrossRef] - Cruz, A.; Muñoz, A.; Zamora, J.L.; Espínola, R. The effect of wind generation and weekday on Spanish electricity spot price forecasting. Electr. Power Syst. Res.
**2011**, 81, 1924–1935. [Google Scholar] [CrossRef] - Dong, Y.; Wang, J.; Jiang, H.; Wu, J. Short-term electricity price forecast based on the improved hybrid model. Energy Convers. Manag.
**2011**, 52, 2987–2995. [Google Scholar] [CrossRef] - Weron, R.; Misiorek, A. Forecasting spot electricity prices: A comparison of parametric and semiparametric time series models. Int. J. Forecast.
**2008**, 24, 744–763. [Google Scholar] [CrossRef][Green Version] - Mun, F.L.C. Short-term forecasting of electricity prices in the Colombian electricity market. IET Gener. Transm. Distrib.
**2009**, 3, 980–986. [Google Scholar] - Mei, J.; He, D.; Harley, R.; Habetler, T.; Qu, G. A random forest method for real-time price forecasting in New York electricity market. In Proceedings of the IEEE PES General Meeting|Conference & Exposition, National Harbor, MD, USA, 27–31 July 2014. [Google Scholar]
- Mandal, P.; Haque, A.U.; Meng, J.; Srivastava, A.K.; Martinez, R. A novel hybrid approach using wavelet, firefly algorithm, and fuzzy ARTMAP for day-ahead electricity price forecasting. IEEE Trans. Power Syst.
**2013**, 28, 1041–1051. [Google Scholar] [CrossRef] - De Marcos, R.A.; Bello, A.; Reneses, J. Short-term forecasting of electricity prices with a computationally efficient hybrid approach. In Proceedings of the 14th International Conference on the European Energy Market (EEM), Dresden, Germany, 6–9 June 2017. [Google Scholar]
- Vaccaro, A.; El-Fouly, T.H.M.; Canizares, C.A.; Bhattacharya, K. Local learning-ARIMA adaptive hybrid architecture for hourly electricity price forecasting. In Proceedings of the IEEE Eindhoven PowerTech, Eindhoven, The Netherlands, 29 June–2 July 2015. [Google Scholar]
- Yan, X.; Chowdhury, N.A. Hybrid SVM & Armax based mid-term electricity market clearing price forecasting. In Proceedings of the IEEE Electrical Power & Energy Conference, Halifax, NS, Canada, 21–23 August 2013. [Google Scholar]
- Skopal, R. Short-term hourly price forward curve prediction using neural network and hybrid ARIMA-NN model. In Proceedings of the International Conference on Information and Digital Technologies, Zilina, Slovakia, 7–9 July 2015. [Google Scholar]
- Wan, C.; Xu, Z.; Wang, Y.; Dong, Z.Y.; Wong, K.P. A hybrid approach for probabilistic forecasting of electricity price. IEEE Trans. Smart Grid
**2014**, 5, 463–470. [Google Scholar] [CrossRef] - Varshney, H.; Sharma, A.; Kumar, R. A hybrid approach to price forecasting incorporating exogenous variables for a day ahead electricity Market. In Proceedings of the IEEE 1st International Conference on Power Electronics, Intelligent Control and Energy Systems (ICPEICES), Delhi, India, 4–6 July 2016. [Google Scholar]
- Tahmasebifar, R.; Sheikh-El-Eslami, M.K.; Kheirollahi, R. Point and interval forecasting of real-time and day-ahead electricity prices by a novel hybrid approach. IET Gener. Transm. Distrib.
**2017**, 11, 2173–2183. [Google Scholar] [CrossRef] - Chinnathambi, R.A. Investigation of forecasting methods for the hourly spot price of the Day-Ahead Electric Power Markets. In Proceedings of the IEEE International Conference on Big Data (Big Data), Washington, DC, USA, 5–8 December 2016. [Google Scholar]
- Historical Real-Time Price Data for Iberian Electricity Market. Available online: http://complatt.smartwatt.net/#/public/home (accessed on 18 June 2018).
- ARIMA Modelling. Available online: http://ucanalytics.com/blogs/step-by-step-graphic-guide-to-forecasting-through-arima-modeling-in-r-manufacturing-case-study-example/ (accessed on 18 June 2018).
- LOWESS Smoothing. Available online: http://www.statisticshowto.com/lowess-smoothing/ (accessed on 18 June 2018).
- Lantz, B. Machine Learning with R; Packt Publishing Ltd.: Birmingham, UK, 2015; Volume 1, ISBN 9788578110796. [Google Scholar]
- Forte, R.M. Mastering Predictive Analytics with R; Packt Publishing Ltd.: Birmingham, UK, 2015; Volume 1, ISBN 9788578110796. [Google Scholar]
- Generalized Linear Model. Available online: https://en.wikipedia.org/wiki/Generalized_linear_model (accessed on 18 June 2018).
- Monteiro, C.; Fernandez-Jimenez, L.A.; Ramirez-Rosado, I.J. Explanatory information analysis for day-ahead price forecasting in the Iberian electricity market. Energies
**2015**, 8, 10464–10486. [Google Scholar] [CrossRef] - García-Martos, C.; Rodríguez, J.; Sánchez, M.J. Mixed models for short-run forecasting of electricity prices: Application for the Spanish market. IEEE Trans. Power Syst.
**2007**, 22, 544–552. [Google Scholar] [CrossRef] - Contreras, J.; Espínola, R.; Member, S.; Nogales, F.J. ARIMA models to predict next-day electricity prices. IEEE Trans. Power Syst.
**2003**, 18, 1014–1020. [Google Scholar] [CrossRef][Green Version] - Catalão, J.P.S.; Mariano, S.J.P.S.; Mendes, V.M.F.; Ferreira, L.A.F.M. Short-term electricity prices forecasting in a competitive market: A neural network approach. Electr. Power Syst. Res.
**2007**, 77, 1297–1304. [Google Scholar] [CrossRef][Green Version] - Lora, A.T.; Santos, J.M.R.; Exposito, A.G.; Ramos, J.L.M.; Santos, J.C.R. Electricity market price forecasting based on weighted nearest neighbors techniques. IEEE Trans. Power Syst.
**2007**, 22, 1294–1301. [Google Scholar] [CrossRef] - Conejo, A.J.; Plazas, M.A.; Espinola, R.; Molina, A.B. Day-ahead electricity price forecasting using the wavelet transform and ARIMA models. IEEE Trans. Power Syst.
**2005**, 20, 1035–1042. [Google Scholar] [CrossRef] - Amjady, N. Day-ahead price forecasting of electricity markets by a new fuzzy neural network. IEEE Trans. Power Syst.
**2006**, 21, 887–896. [Google Scholar] [CrossRef] - Pindoriya, N.M.; Singh, S.N.; Singh, S.K. An adaptive wavelet neural network-based energy price forecasting in electricity markets. IEEE Trans. Power Syst.
**2008**, 23, 1423–1432. [Google Scholar] [CrossRef] - Catalão, J.P.S.; Pousinho, H.M.I.; Mendes, V.M.F. Neural networks and wavelet transform for short-term electricity prices forecasting. In Proceedings of the 15th International Conference on Intelligent System Applications to Power Systems, Curitiba, Brazil, 8–12 November 2009. [Google Scholar]
- Pousinho, H.M.I.; Mendes, V.M.F.; Catalão, J.P.S. Short-term electricity prices forecasting in a competitive market by a hybrid intelligent approach. Energy Convers. Manag. J.
**2011**, 39, 29–35. [Google Scholar] - Shafie-Khah, M.; Moghaddam, M.P.; Sheikh-El-Eslami, M.K. Price forecasting of day-ahead electricity markets using a hybrid forecast method. Energy Convers. Manag.
**2011**, 52, 2165–2169. [Google Scholar] [CrossRef] - Catalão, J.P.S.; Pousinho, H.M.I.; Mendes, V.M.F. Hybrid wavelet-PSO-ANFIS approach for short-term electricity prices forecasting. IEEE Trans. Power Syst.
**2011**, 26, 137–144. [Google Scholar] [CrossRef] - Amjady, N.; Keynia, F. Day-ahead price forecasting of electricity markets by mutual information technique and cascaded neuro-evolutionary algorithm. IEEE Trans. Power Syst.
**2009**, 24, 306–318. [Google Scholar] [CrossRef]

**Figure 2.**Comparison of MAPE for one week (24 July 2015 to 30 July 2015) to predict day-ahead price (31 July 2015).

**Figure 3.**Comparison of MAPE for two weeks (17 July 2015 to 30 July 2015) to predict day-ahead price (31 July 2015).

**Figure 4.**Comparison of MAPE for three weeks (10 July 2015 to 30 July 2015) to predict day-ahead price (31 July 2015).

**Figure 5.**Comparison of MAPE for one month (1 July 2015 to 30 July 2015) to predict day-ahead price (31 July 2015).

**Figure 6.**Comparison of MAPE for 45 days (16 June 2015 to 30 July 2015) to predict day-ahead price (31 July 2015).

**Figure 7.**Comparison of MAPE for 60 days (1 June 2015 to 30 July 2015) to predict day-ahead price (31 July 2015).

**Figure 8.**Comparison of MAPE for 75 days (17 May 2015 to 30 July 2015) to predict day-ahead price (31 July 2015).

**Figure 9.**Comparison of MAPE for 90 days (1 May 2015 to 30 July 2015) to predict day-ahead price (31 July 2015).

**Figure 10.**Comparison of MAPE for all dataset from one week to 75 days to predict day-ahead price (31 July 2015).

**Figure 11.**Comparison of MAPE for 1, 2, 3 and 6-month weekdays dataset to predict day-ahead price (31 July 2015).

**Figure 12.**Comparison of MAPE for 1, 2, 3 and 6-month weekend dataset to predict day-ahead price (26 July 2015).

Data Duration | p | d | q | MAPE |
---|---|---|---|---|

One week | 4 | 1 | 3 | 5.36 |

Two weeks | 2 | 0 | 1 | 4.23 |

Three weeks | 4 | 0 | 4 | 4.07 |

One month | 5 | 0 | 4 | 5.64 |

45 days | 2 | 1 | 2 | 2.7 |

60 days | 1 | 1 | 0 | 1.99 |

75 days | 4 | 1 | 3 | 1.99 |

90 days | 4 | 1 | 3 | 2.80 |

Weekday-one month | 5 | 0 | 4 | 8.16 |

Weekday-two months | 3 | 1 | 1 | 1.81 |

Weekday-three months | 2 | 1 | 2 | 3.58 |

Weekday-six months | 1 | 1 | 0 | 4.48 |

Weekend-one month | 2 | 0 | 1 | 13.07 |

Weekend-two months | 2 | 1 | 3 | 9.94 |

Weekend-three months | 5 | 1 | 1 | 9.73 |

Weekday-six months | 2 | 1 | 2 | 9.91 |

Variable No. | Description |
---|---|

1, 2 | Hourly Price D, Hourly Price D-6 |

3, 4 | Hourly Power Demand D-1 & D-6 |

5, 6 | Hourly Hydropower Generation D-1 & D-6 |

7, 8 | Hourly Solar Power D-1 & D-6 |

9, 10 | Hourly Coal Power Generation D-1 & D-6 |

11, 12 | Hourly Wind Power Generation D-1 & D-6 |

13, 14 | Hourly Combined Cycle Power Generation D-1 & D-6 |

15, 16, 17 | Hourly Temperature, Wind speed, Radiation D+1 |

MAPE | ARIMA | ARIMA-GLM | ARIMA-SVM | ARIMA-RF |
---|---|---|---|---|

Short-Term Price Forecast (Day-Ahead) | ||||

${\mathrm{MAPE}}_{1week}$ | 5.36 | 5.00 | 3.73 | 5.24 |

${\mathrm{MAPE}}_{2weeks}$ | 4.23 | 4.43 | 3.98 | 4.01 |

${\mathrm{MAPE}}_{3weeks}$ | 4.07 | 4.14 | 3.64 | 3.69 |

${\mathrm{MAPE}}_{1month}$ | 5.64 | 5.54 | 5.05 | 5.44 |

${\mathrm{MAPE}}_{45days}$ | 2.7 | 2.54 | 2.49 | 2.38 |

${\mathrm{MAPE}}_{60days}$ | 1.99 | 1.92 | 2.037 | 2.027 |

${\mathrm{MAPE}}_{75days}$ | 1.99 | 1.92 | 2.009 | 2.2263 |

**Table 4.**Comparison of day-ahead forecasting performance of several hybrid models for 90 days of dataset using 4 variables (Hourly price D, Hourly price D-6, Hourly power demand D-1 & D-6).

MAPE | ARIMA | ARIMA-GLM | ARIMA-SVM | ARIMA-LOWESS | ARIMA-RF |
---|---|---|---|---|---|

${\mathrm{MAPE}}_{90days}$ | 2.80 | 2.59 | 2.73 | 2.66 | 3.12 |

**Table 5.**Comparison of day-ahead forecasting performance of several hybrid models for weekday dataset using 17 variables.

MAPE | ARIMA | ARIMA-GLM | ARIMA-SVM | ARIMA-RF |
---|---|---|---|---|

${\mathrm{MAPE}}_{1month}$ | 8.16 | 8.30 | 7.41 | 7.01 |

${\mathrm{MAPE}}_{2month}$ | 1.81 | 1.86 | 1.84 | 2.33 |

${\mathrm{MAPE}}_{3month}$ | 3.58 | 3.83 | 3.82 | 4.72 |

${\mathrm{MAPE}}_{6month}$ | 4.48 | 4.54 | 4.62 | 5.78 |

**Table 6.**Comparison of day-ahead forecasting performance of several hybrid models for weekend dataset using 10 variables.

MAPE | ARIMA | ARIMA-GLM | ARIMA-SVM | ARIMA-RF |
---|---|---|---|---|

${\mathrm{MAPE}}_{1month}$ | 13.07 | 12.4 | 12.01 | 13.7 |

${\mathrm{MAPE}}_{2month}$ | 9.94 | 9.15 | 9.26 | 9.52 |

${\mathrm{MAPE}}_{3month}$ | 9.73 | 9.22 | 9.15 | 9.19 |

${\mathrm{MAPE}}_{6month}$ | 9.91 | 9.63 | 9.53 | 9.88 |

**Table 7.**Comparison of MAPE results for two-stage ARIMA model with/without explanatory variables in Stage-2.

MAPE | ARIMA | ARIMA-ARIMA (with Explanatory Variables in Stage-2) | ARIMA-ARIMA (without Explanatory Variables in Stage-2) |
---|---|---|---|

${\mathrm{MAPE}}_{1week}$ | 5.36 | 4.66 | 5.34 |

${\mathrm{MAPE}}_{2weeks}$ | 4.23 | 4.44 | 3.79 |

${\mathrm{MAPE}}_{3weeks}$ | 4.07 | 4.14 | 4.02 |

${\mathrm{MAPE}}_{1month}$ | 5.64 | 5.54 | 5.65 |

${\mathrm{MAPE}}_{45days}$ | 2.7 | 2.54 | 2.73 |

${\mathrm{MAPE}}_{60days}$ | 1.99 | 1.78 | 1.91 |

${\mathrm{MAPE}}_{75days}$ | 1.99 | 1.84 | 1.98 |

Methods | MAPE |
---|---|

Mixed Model [46]—one week | 14.90 |

ARIMA with 2 Variables—five months [47] | 13.39 |

Neural Network—40 days [48] | 11.40 |

Weighted Nearest Neighbor—23 months [49] | 10.89 |

Wavelet-ARIMA with 4 Variables—47 days [50] | 10.70 |

Fuzzy Neural Network [51] | 9.84 |

Adaptive Wavelet Neural Network with 2 variables [52] | 9.64 |

Neural network Wavelet Transform with 1 variable [53] | 9.5 |

WNF with 1 variable—42 days [54] | 9.47 |

Elman Network [55] | 9.09 |

Hybrid Intelligent systems with 3 Variables | 7.47 |

Wavelet-ARIMA-RBFN | 6.76 |

Hybrid wavelet-PSO-ANFIS [56] | 6.50 |

Cascaded Neuro-evolutionary Algorithm with 2 variables-50 days [57] | 5.79 |

MAPE | ARIMA | ARIMA-GLM | ARIMA-SVM | ARIMA-RF |
---|---|---|---|---|

Short-Term Price Forecast (Day-Ahead) | ||||

${\mathrm{MAPE}}_{1week}$ | Average | Average | Good | Average |

${\mathrm{MAPE}}_{2weeks}$ | Good | Good | Good | Good |

${\mathrm{MAPE}}_{3weeks}$ | Good | Good | Good | Good |

${\mathrm{MAPE}}_{1month}$ | Average | Average | Average | Average |

${\mathrm{MAPE}}_{45days}$ | Good | Good | Good | Good |

${\mathrm{MAPE}}_{60days}$ | Good | Good | Good | Good |

${\mathrm{MAPE}}_{75days}$ | Good | Good | Good | Good |

Parameter | ARIMA | ARIMA-GLM | ARIMA-SVM | ARIMA-RF |
---|---|---|---|---|

Short-Term Price Forecast (Day-Ahead) | ||||

${Correlation}_{1week}$ | 0.941 | 0.947 | 0.964 | 0.946 |

${Correlation}_{2weeks}$ | 0.958 | 0.970 | 0.973 | 0.957 |

${Correlation}_{3weeks}$ | 0.963 | 0.971 | 0.969 | 0.963 |

${Correlation}_{1month}$ | 0.966 | 0.971 | 0.967 | 0.962 |

${Correlation}_{45days}$ | 0.977 | 0.979 | 0.976 | 0.974 |

${Correlation}_{60days}$ | 0.982 | 0.983 | 0.982 | 0.981 |

${Correlation}_{75days}$ | 0.979 | 0.981 | 0.979 | 0.976 |

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## Share and Cite

**MDPI and ACS Style**

Angamuthu Chinnathambi, R.; Mukherjee, A.; Campion, M.; Salehfar, H.; Hansen, T.M.; Lin, J.; Ranganathan, P. A Multi-Stage Price Forecasting Model for Day-Ahead Electricity Markets. *Forecasting* **2019**, *1*, 26-46.
https://doi.org/10.3390/forecast1010003

**AMA Style**

Angamuthu Chinnathambi R, Mukherjee A, Campion M, Salehfar H, Hansen TM, Lin J, Ranganathan P. A Multi-Stage Price Forecasting Model for Day-Ahead Electricity Markets. *Forecasting*. 2019; 1(1):26-46.
https://doi.org/10.3390/forecast1010003

**Chicago/Turabian Style**

Angamuthu Chinnathambi, Radhakrishnan, Anupam Mukherjee, Mitch Campion, Hossein Salehfar, Timothy M. Hansen, Jeremy Lin, and Prakash Ranganathan. 2019. "A Multi-Stage Price Forecasting Model for Day-Ahead Electricity Markets" *Forecasting* 1, no. 1: 26-46.
https://doi.org/10.3390/forecast1010003