## 1. Introduction

#### Main Idea

## 2. Data

#### 2.1. Institutional Details of the German Electricity Market

#### 2.2. Data Description

#### 2.3. Data Filtering

## 3. Methodology

#### 3.1. General Description of the Modified X-Model

#### 3.2. Transformation of the Auction Curves

#### 3.3. Defining the Price Classes

#### 3.4. Time Series Model

**β**-coefficients, we used the R-package

`glmnet`, which was described in, e.g., [39]. The corresponding mathematical representation of scaled and estimated $\hat{\stackrel{\sim}{\mathit{\beta}}}$ coefficients can be written as follows:

#### 3.5. Supply Curve Reconstruction

## 4. Results

## 5. Conclusions

## Funding

## Acknowledgments

## Conflicts of Interest

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Sample Availability: Samples of the compounds as well as the source code are available from the authors for review purposes. |

**Figure 1.**A wholesale market equilibrium in the EPEXSPOTSEon 2017-02-01 at 00:00:00 (left plot) vs. its manipulated form with an inelastic demand curve (right plot).

**Figure 2.**A wholesale market equilibrium in the EPEX SPOT SE on 2017-02-01 at 00:00:00 with transformed auction curves and highlighted price classes. The left-hand side of the figure shows the entire auction curves recorded at the time point. The right-hand side of the figure plots the same curves, but focuses on the equilibrium between them.

**Figure 3.**Market equilibrium forecast on 2017-02-01 at 10-00-00. The left-hand side of the figure shows the entire auction curves recorded at the time point. The right-hand side of the figure plots the same curves, but focuses on the equilibrium between them.

**Figure 4.**Hourly MAE (left-hand side) and RMSE (right-hand side) values of the modified X-model ($xmo{d}^{modified}$), the original X-model ($xmo{d}^{original}$), and the combined X-model ($xmo{d}^{combined}$).

**Figure 5.**p-values for each hour of the day of the comparison of the models $xmo{d}^{modified}$ vs. $xmo{d}^{combined}$ according to the DM-test. As can be seen from the figure, the modified X-model outperformed the combined X-model during most hours of the day.

−500.0 | −250.0 | −100.1 | −76.1 | −15.8 | 3.6 | 10.0 | 13.6 | 19.2 | 22.3 |

25.9 | 30.0 | 34.0 | 39.1 | 49.4 | 81.0 | 200.0 | 1871.9 | 3000.0 |

**Table 2.**Comparison of the yearly MAE and RMSE values of the naivebenchmark, the original X-model ([22]), the modified X-model with an inelastic demand curve, and an equally weighted mixture of the original and the modified X-models.

MAE | RMSE | Average Execution Time (min) | |
---|---|---|---|

$naive$ | 9.97 | 11.90 | - |

$xmo{d}^{original}$. | 6.21 | 7.54 | 4.34 |

$xmo{d}^{modified}$. | 5.12 | 6.45 | 1.40 |

$xmo{d}^{combined}$. | 5.28 | 6.47 | - |

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