# Walking Back the Data Quantity Assumption to Improve Time Series Prediction in Deep Learning
## 4 Dataset Details and Performance Metrics  
### Dataset  
This section describes the time series used in the experimentation process to verify the results with the ANNs used: MLP, LSTM, and transformer. These are data with different characteristics, especially the number of observations, to check how the new methodology influences when it comes to obtaining the best results. The first time series included in the study is the time series with prices from NEMO (nominated electricity market operator) for the management of the daily and intraday market for electricity prices. The large number of observations contained in this dataset allows a contrast with smaller time series. The data are composed of information between 13 November 2019, and 24 October 2023. The complex patterns of this series make it suitable for prediction with the different models used. To test the robustness of the proposed model, different datasets are included. The second set is made up of data related to the West Texas intermediate crude price index (WTI) obtained through the Thomson Eikon Reuters platform. The data have a daily timeline that covers from 10 January 1983 to 15 June 2022. WTI prices are the most used spot oil price, along with Brent spot prices as a reference to set the price of oil. The third dataset includes the one corresponding to the Apple stock index with daily data from 7 May 2004 to 8 May 2024. These data show a slight increasing trend, which helps to validate the model in different cases. Lastly, data relating to the gold price index using the XAU/USD pair are included with daily data from 13 May 2015 to 15 June 2022. Figures 4-7 illustrate the graphs of each time series. Figure 4a,c,e reflect the performance of the methodology in the iteration in which the most adjusted metrics were obtained, while Figure 4b,d,f represent the result obtained using the total number of observations available for the GOLD time series corresponding to the MLP, LSTM, and transformer models, respectively. Figures 5-7 follow the same structure for the WTI, Apple, and OMIE time series respectively. Notably, the WTI time series (Figure 5) exhibits an unusual peak in the middle, which poses a challenge for the proposed methodology. In contrast, the other time series do not display irregular patterns that could complicate the methodology's application. Statistical analyses confirm that the datasets remain stable and representative across varying observation sizes, supporting the validity of the experimental setup and ensuring the reliability of the results. This comprehensive approach reinforces the robustness of the findings, particularly regarding the relationship between dataset size and model performance. Figure 4: \(Cont\). Figure 4: Gold results. Figure 5: _Cont._  
Figure 5: WTI results. Figure 6: Apple results. The choice of these time series is due to the different characteristics of each of them, especially valuing the different number of observations that make them up. Table 1 shows the number of observations in each time series, in addition to the division of each of these by the methodology used and the quantity used in each of the observations. The data have been split randomly to create the train and test partitions. To ensure replicability, the same seed has been established for random selection in each method. The experiments included an in-depth analysis of frequency distributions to identify potential biases and dispersion within the time series data. For instance, the OMIE time series contained numerous values of zero or close to zero, which complicated the calculation of certain metrics, such as the mean absolute percentage error (MAPE). Consequently, the MAPE metric was not calculated for the OMIE time series. This behavior necessitated specific adjustments to the metrics employed for model performance evaluation. Additionally, series such as WTI and Apple displayed heterogeneous patterns characterized by episodes  
Figure 7: OMIE results. of high volatility followed by relatively stable periods.