# Conditional Temporal Aggregation for Time Series Forecasting Using Feature-Based Meta-Learning
## 6 Conclusions  
We have proposed a meta-learner that can be used to either select the most appropriate temporal aggregation level for producing forecasts or to derive weights that properly combine the forecasts generated at various levels. To do so, the meta-learner extracts a rich set of time series features and correlates them to post-sample forecasting accuracy, thus allowing for conditional forecast selection or combination.  
Our results indicate that conditional (multiple) temporal aggregation can outperform both conventional forecasting and established methods used for applying temporal aggregation. The improvements are more significant for fast-moving data where patterns are easier to identify, but can be realized for slow-moving data as well. As expected, conditional multiple temporal aggregation performs better on average than conditional temporal aggregation. However, we find that in many cases, selecting the \"best\" aggregation level is feasible, leading to better forecasts than forecasting at the original data frequency.  
Figure 4: MCB test of the methods utilized within the study for forecasting the series of the M4 (**top**) and M5 (**bottom**) competitions.  
Future work could focus on extending and improving the proposed approach. This could include the investigation of alternative classification methods (e.g., logistic regression, extreme gradient boosting, and neural networks) and the development of alternative schemes for transforming classification probabilities into combination weights. Moreover, since the potential benefits of (multiple) temporal aggregation seem to magnify for time series of relatively higher frequencies, the proposed meta-learner could be tested for data that are sampled on an hourly or even minute basis. To the best of our knowledge, the work performed in the field of temporal aggregation has insufficiently covered said applications, despite the fact that methods such as the one proposed in the present paper could improve forecasting accuracy through a conditional aggregation of time series patterns observed at different temporal aggregation levels.  
Conceptualization, A.K., E.S. and V.A.; methodology, A.K., E.S. and V.A.; software, A.K. and E.S.; validation, A.K. and E.S.; formal analysis, A.K. and E.S.; investigation, A.K., E.S. and V.A.; resources, V.A.; data curation, A.K., E.S. and V.A.; writing--original draft preparation, A.K., E.S. and V.A.; writing--review and editing, A.K., E.S. and V.A.; visualization, A.K.; supervision, V.A.; project administration, V.A. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
The data sets of the M4 and the M5 forecasting competitions are publicly available and can be downloaded from the GitHub repository ([[https://github.com/Mcompetitions](https://github.com/Mcompetitions)]([https://github.com/Mcompetitions](https://github.com/Mcompetitions)), accessed on 10 April 2023) devoted to the M competitions.  
The authors declare no conflicts of interest.  
The following abbreviations are used in this manuscript:  
\begin{tabular}{l l} CMTA & Conditional multiple temporal aggregation \\ CTA & Conditional temporal aggregation \\ ETS & Exponential smoothing (error, trend, seasonality) \\ EW & Equal Weights \\ MASE & Mean absolute scaled error \\ ML & Machine learning \\ PW & Probability-based weights \\ PSTR & Probability-based structural scaling \\ RMSSE & Root mean squared scaled error \\ SBA & Syntetos-Boylan Approximation \\ STR & Structural scaling \\ \end{tabular}