## 6 Conclusions  
In this work, we compared the forecasting performance of statistical and deep learning methods on time series data from an aggregated mobile phone activity dataset. The results of our study show that both statistical and deep learning methods have advantages and limitations.  
The main conclusions that we reach with this research work are that deep learning methods are easier to apply on time series forecasting tasks. In particular in tasks such as the one we explored in this paper in which the forecasting service should be provided for thousands of cells which may be very different one from the other in their time series. Besides simplicity, deep learning methods offer similar results to the most popular statistical methods such as ARIMA with the additional advantage of lowering the maximum error. Our experiments and in particular the MAXAE, have shown that deep learning methods are robust and avoid large errors mainly due to their ability to learn from data and also because of special data preparation techniques such as STL decomposition. Moreover, the deep learning methods applied in this study have shown to be more robust to parameter selection with respect to statistical approaches. They seem to be a one-size-fits-all solution which is the perfect match in a context such as ours. In addition to this, deep learning methods show to have greater benefits from the availability of larger data sets thus improving their forecasting performance when compared with statistical methods which typically do not improve their results when more data is available.  
Statistical methods can instead give more precise results with lower forecasting errors on average but they are not the most suitable methods to use for our forecasting scenario. We reach this conclusion based on several findings and the most important ones are as follows. To use statistical methods successfully we need to have a very good knowledge of the data domain. Moreover, in our case we had to perform a careful analysis with time-consuming grid searching techniques for finding the optimal parameters of the statistical models such as ARIMA and ETS. On the contrary, deep learning methods do not require an expertise of data domain. They did not require us to go through any particular feature engineering process which may reveal be time-consuming and prone to errors due to arbitrary assumptions. Finally, given the strong linear relationship that exists in datasets such as aggregated mobile phone data, we reach the conclusion that statistical methods such as ARIMA are not able to perform significantly better than deep learning ones. This is particularly true when there are time-to-deliver constraints for the forecasting service and there is a need to minimize the maximum forecasting error. If these issues are a problem for the specific application then deep learning methods become a more time efficient and effective tool to use.  
Investigation, A.C.; Methodology, M.L.; Project administration, M.M. and F.Z. All authors have read and agreed to the published version of the manuscript.  
Work supported by the POR-FESR 2014-2020 Project: Policy Support System for smart city data governance-POLIS-EYE. PG/2018/631990. CUP E21F18000200007.  
There are no conflicts of interest between the authors and the funding parties.