# Conditional Temporal Aggregation for Time Series Forecasting Using Feature-Based Meta-Learning
## 3 Proposed Method  
As discussed in Section 2, various approaches can be used to combine or to select forecasts (selection can be considered as an extreme combination case where the total weight is assigned to a single forecast and, as a result, the rest of the forecasts are discarded by receiving a weight of zero). A simple yet effective approach is to average all base forecasts available, since, due to the uncertainty present, there is often no guarantee that the \"optimal\" forecast combination will outperform the equal-weighted one [3]. Similarly, one may decide to combine the base forecasts using other standard operators, such as the median [41] or the mode [42], as they are less sensitive to outliers and asymmetric distributions. Nevertheless, when there is strong evidence that some forecasts are more accurate than others, forecasters usually prefer to weight the base forecasts using either linear (e.g., optimal combining and variable weighting methods) or nonlinear combination (e.g., neural network methods and self-organizing algorithms) schemes [38]. In such cases, the weights of combining are typically determined by evaluating the in-sample accuracy of the base forecasts [39; 40], but cross-validation techniques [43] can also be used to better simulate their post-sample performance [1]. As a result, forecasts that are regarded as more accurate are weighted more in the combination compared to less accurate ones. An interesting alternative to combine or to select forecasts involves the examination of the characteristics of the time series being predicted. The key idea behind this approach is that, depending on the characteristics of the series, different types of forecasts may be more relevant. [PERSON] [44] and [PERSON] [45] used linear regression and discriminant analysis methods to predict the performance of various forecasts, thus providing some early selection rules. Similarly, [PERSON] and [PERSON] [46], [PERSON] [47], [PERSON] et al. [48], and [PERSON] et al. [49] employed rule-based forecasting and expert systems to combine or to select forecasts depending on the data conditions. [PERSON] et al. [25] considered a set of time series features and the forecasting horizon to select the most appropriate forecast concluding that there are useful feature cases both for fast- and slow-moving data. More recently, [PERSON] et al. [50] and [PERSON] et al. [51] explored the characteristics of the time series used in popular forecasting competitions, including the M3 and M4 [4], confirming that the relative performance of different forecasting methods depends on the particularities of the data. Building on this concept, [PERSON] et al. [30] used the M4 data set to train a meta-learner that assigned combination weights to nine different forecasting methods by linking their performance, measured through cross-validation, with the features of the series. The meta-learner, which was an extreme gradient boosted tree, was proved very successful, winning the second place in the M4 competition. Similarly, [PERSON] et al. [26] used a Bayesian multivariate regression method to construct a feature-based meta-learner that predicts the performance of each forecasting method, thus providing evidence about which base forecast(s) should be selected or combined. In cross-sectional hierarchical forecasting settings, [PERSON] et al. [28] used ML classification methods to determine, based on the characteristics of the series involved in the hierarchy, which reconciliation method (e.g., bottom-up, top-down, and optimal) should be preferred. There are many advantages of using ML meta-learners to combine or to select forecasts over utilizing other approaches [23]. First, in contrast to expert systems and heuristic rule-based forecasting methods, the rules of the meta-learners are explicitly derived by the available data instead of being defined by experts, whose insights may be biased or focused on particular applications and data sets.