# 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

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**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