# Short-Term Electricity Price Forecasting with Recurrent Regimes and Structural Breaks

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## Abstract

**:**

## 1. Introduction

- Prior to the NN forecast, the NN training period, which is initially set to a very large window, is filtered by means of a structural break analysis method and periods where prices significantly differ from those prior to the forecasting period (i.e., most recent prices) are discarded.
- Furthermore, the hourly trends in the actual forecasting period according to market regime related variables are evaluated via a K-means clustering procedure. The hours of the initial NN calibration period where the assigned cluster coincides with that of the hours in the forecasting period are included in the previously filtered calibration period by the structural break analysis method. This combination of training window selection techniques is carried out ex-ante and therefore provides a dynamic calibration dataset.
- The proposed set of methodologies is backtested on the real and full-scale Iberian electricity market of 2017. The performance of this approach is compared with that of other well-recognised forecasting models.

## 2. Proposed Methodology

#### 2.1. Cost-Production Optimisation Model

#### 2.2. Period Selection

#### 2.2.1. Structural Breaks

#### 2.2.2. Hourly Clustering

#### 2.2.3. Neural Network Validation Set

#### 2.3. Artificial Neural Network Model

- Expected values of demand, wind and solar generation
- Expected mean temperature in the Iberian Peninsula
- Two dummy variables corresponding to working days or a Sunday/holiday, thus Saturdays would correspond to both dummy variables being false
- Actual electricity market prices with the following lags: one day, two days, one week and two weeks
- Commodity related month-ahead forward prices: API2 coal, NBP natural gas and European CO
_{2}emission allowances - Day-ahead Iberian electricity market futures
- Fundamental model output variables: market-clearing prices; and coal, CCGT and hydro production levels.

#### 2.4. Model Performance Metrics and Evaluation Criteria

## 3. Case Studies, Results and Discussion

_{2}emission allowance prices began in the late summer of 2017. More specifically, these prices rose by approximately 25% throughout the year of 2017. Therefore, this case study poses a highly challenging task with disruptions and evolving changes and is, therefore, a suitable test of the methodology proposed in this paper.

- Stage 0: A base hybrid fundamental-econometric model without filtering any periods and variables and using 120 days of calibration data, although a limited filtering procedure in winter 2017 reduced this data length by roughly 70%. This coincides with the Proposed Model 2 that was presented in [19].
- Stage 1: 13 months of calibration data are used and these are filtered via the structural breaks technique.
- Stage 2: The K-means hourly clustering procedure is added to the calibration period selection method.

_{i}, i.e., the Proposed Model at its Stage i. As in other works, for instance [11], the performance of these models has been analysed for every season of the year and compared with that of six other electricity price forecasting models, some of which correspond to well-established methodologies in the literature. The first chosen benchmark model (Benchmark 1 or BM

_{1}) consists of the proposed simple average of [19] between the forecasts of a pure NN model and the base hybrid fundamental-econometric model (PMS

_{0}). Benchmark two (BM

_{2}) only involves this pure NN model that utilises the same input variables as BM

_{1}/PMS

_{0}(except those pertaining to the fundamental model) and the same calibration window. This 120-day window includes four months within the 13-month window established in this work, more specifically, the 13th, 12th, 2nd and 1st month prior to the forecasting day [19].

_{3}) is related to a linear regression model with several autoregressive terms and exogenous components. This ARX model, introduced in [32] and recently utilised in [15], includes a logarithmic transform that was modified so as to account for the lower price cap of zero in the Iberian electricity market:

_{4}) is the extension of BM

_{3}as per the work presented in [15], which performs a weighted average of forecasts from the ARX model of Equation (1) across the following calibration windows (in terms of days prior to the forecast day): 56, 84, 112, 714, 721 and 728 days. The weights of these six forecasts are computed by means of an inverse MAE weighting procedure when testing the ARX models on the day prior to the forecast day.

_{5}) is related to a SARIMAX model, whose SARIMA noise presents the following notation: SARIMA(1,0,0)

_{168}(1,0,2)

_{24}(1,0,0)

_{1}. A daily and weekly seasonality was considered, as well as the expected demand as an exogenous variable. This model was created following [34,35], with the Box-Jenkins methodology. Furthermore, the Box-Cox transformation was used to stabilise the price variance [36]. The final benchmark (BM

_{6}) is related to a simple naïve approach that sets the forecast to the actual electricity price value corresponding to the previous week.

_{0}, the implementation of the structural breaks technique increased the NN training set by well beyond the predefined number of 120 days that was established in [19]. The reason behind the reduced dataset during the 2017 winter is due to its high instability, and it was observed in [19] that a reduction of the 120-day dataset provided useful results. This agrees with the rationale that consists of increasing adaptability on unstable periods by reducing the calibration window in order to remove structural breaks from the input dataset. However, in this work, an average dataset of 152.9 days yields lower forecasting errors. Furthermore, PMS

_{1}discards most of the previous winter, which is considerably different from the 2017 winter as depicted in Figure 3. This also seems to be the case for spring, as the 2016 spring yielded approximately twice as much hydro generation as the 2017 spring. In general, the structural breaks algorithm provides a generally lower error throughout 2017. However, summer 2017 appears to be the exception, where prices are relatively stable and thus, it lacks room for improvement, as proven by the generally low errors yielded by most models.

_{1}’s calibration dataset with the hourly clustering technique of PMS

_{2}further reduces the overall forecasting error. This is more notable during winter, where the average calibration dataset is greatly increased to 288.8 days. As for the other seasons, a calibration dataset of approximately one year proves to be beneficial for electricity price forecasting with NN models even with the hourly arrangement and does not seem to cause any overfitting issues. Although PMS

_{2}yields a lower error overall, the statistical significance of these error measures must be verified in order to confirm its superiority against its competitors, especially the highest-ranked models according to Table 1. Therefore, a DM test was carried out for PMS

_{2}against every other model. The DM test statistic is evaluated with a 5% significance level, such that a DM statistic < −1.96 implies significant outperformance. The results of the DM test statistic are shown in Table 3.

_{2}was unable to significantly outperform. The comparison with PMS

_{0}suggests that the increase in calibration data window lengths does not significantly contribute to summer forecasts, albeit not detrimental to the accuracy. This may also imply that a robust calibration period selection is not highly crucial in such a stable market regime. Therefore, the same conclusion can be drawn from the summer comparison with PMS

_{1}. Furthermore, the DM statistic value in autumn when compared with PMS

_{1}may indicate that the information provided by the hourly clustering method is not significantly different than that provided by the structural breaks technique. However, these values indicate that PMS

_{2}is significantly outperforming all other models throughout the year in 2017.

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

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**Table 1.**Forecast error measures for the proposed and benchmark models: MAPE (%), MAE & RMSE (€/MWh).

Model | Winter | Spring | Summer | Autumn | Entire 2017 | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

MAPE | MAE | RMSE | MAPE | MAE | RMSE | MAPE | MAE | RMSE | MAPE | MAE | RMSE | MAPE | MAE | RMSE | |

PMS [19]_{0}—Base model | 11.68 | 4.756 | 5.479 | 8.106 | 2.882 | 3.407 | 4.450 | 2.070 | 2.517 | 6.812 | 3.453 | 4.129 | 7.744 | 3.282 | 3.874 |

PMS_{1}—Structural breaks | 11.02 | 4.266 | 4.917 | 7.706 | 2.487 | 2.960 | 4.501 | 2.063 | 2.509 | 6.237 | 3.150 | 3.820 | 7.348 | 2.984 | 3.543 |

PMS_{2}—Hourly clustering | 10.05 | 4.133 | 4.785 | 7.303 | 2.433 | 2.892 | 4.467 | 2.045 | 2.504 | 6.284 | 3.139 | 3.818 | 7.012 | 2.930 | 3.492 |

BM_{1}—½(PMS [19]_{0} + BM_{2}) | 11.30 | 4.610 | 5.334 | 7.902 | 2.832 | 3.349 | 4.477 | 2.079 | 2.525 | 6.756 | 3.409 | 4.069 | 7.591 | 3.224 | 3.810 |

BM [19]_{2}—Pure NN | 11.12 | 4.562 | 5.308 | 7.804 | 2.826 | 3.342 | 4.605 | 2.136 | 2.588 | 6.834 | 3.440 | 4.089 | 7.575 | 3.233 | 3.823 |

BM [32]_{3}—ARX | 16.79 | 6.838 | 7.809 | 13.58 | 4.765 | 5.552 | 7.153 | 3.262 | 3.885 | 10.51 | 5.066 | 6.055 | 11.99 | 4.972 | 5.814 |

BM [15]_{4}—W. ARX | 16.27 | 6.390 | 7.314 | 13.21 | 4.500 | 5.268 | 7.015 | 3.211 | 3.857 | 10.14 | 4.880 | 5.874 | 11.64 | 4.736 | 5.568 |

BM_{5}—SARIMAX | 15.06 | 8.113 | 10.84 | 9.293 | 4.150 | 5.585 | 5.097 | 2.473 | 4.531 | 7.654 | 4.454 | 4.959 | 9.248 | 4.780 | 6.460 |

BM_{6}—Naïve approach | 25.93 | 10.53 | 11.48 | 17.55 | 6.225 | 7.092 | 9.343 | 4.266 | 5.030 | 12.82 | 6.387 | 7.567 | 16.37 | 6.828 | 7.773 |

Model | Winter | Spring | Summer | Autumn | Overall |
---|---|---|---|---|---|

PMS [19]_{0}, BM_{1} & BM_{2} | 36.67 | 120.0 | 120.0 | 120.0 | 99.17 |

PMS (Figure 3)_{1} | 152.9 | 237.0 | 324.7 | 300.5 | 254.2 |

PMS (Figure 4)_{2} | 288.8 | 324.5 | 344.7 | 348.1 | 326.7 |

Model Comparison | Winter | Spring | Summer | Autumn | Entire 2017 |
---|---|---|---|---|---|

PMS_{2} vs. PMS_{0} | −8.834 | −12.31 | −0.975 | −6.787 | −14.75 |

PMS_{2} vs. PMS_{1} | −2.903 | −3.199 | −1.833 | −0.436 | −3.917 |

PMS_{2} vs. BM_{1} | −6.528 | −8.042 | −2.883 | −5.726 | −11.29 |

PMS_{2} vs. BM_{2} | −6.316 | −11.36 | −3.262 | −6.877 | −13.18 |

PMS_{2} vs. BM_{3} | −21.54 | −28.70 | −22.94 | −21.69 | −44.76 |

PMS_{2} vs. BM_{4} | −18.78 | −26.37 | −21.18 | −19.59 | −40.67 |

PMS_{2} vs. BM_{5} | −21.21 | −17.96 | −4.454 | −16.85 | −29.70 |

PMS_{2} vs. BM_{6} | −34.44 | −33.17 | −27.75 | −28.66 | −58.82 |

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**MDPI and ACS Style**

Marcos, R.A.d.; Bunn, D.W.; Bello, A.; Reneses, J.
Short-Term Electricity Price Forecasting with Recurrent Regimes and Structural Breaks. *Energies* **2020**, *13*, 5452.
https://doi.org/10.3390/en13205452

**AMA Style**

Marcos RAd, Bunn DW, Bello A, Reneses J.
Short-Term Electricity Price Forecasting with Recurrent Regimes and Structural Breaks. *Energies*. 2020; 13(20):5452.
https://doi.org/10.3390/en13205452

**Chicago/Turabian Style**

Marcos, Rodrigo A. de, Derek W. Bunn, Antonio Bello, and Javier Reneses.
2020. "Short-Term Electricity Price Forecasting with Recurrent Regimes and Structural Breaks" *Energies* 13, no. 20: 5452.
https://doi.org/10.3390/en13205452