## 5 Discussion and Practical Evaluation  
In this paper, a series of works on different areas of time series analysis and forecasting were selectively presented, with the aim of comparing the classic ARIMA forecasting algorithms with machine learning and deep learning models. As we see in the consolidated representation of these tasks in Tables 2-5 the used metrics, based on which the comparison of each algorithm with the ARIMA technique was performed, are similar for the majority of the tasks. In the comparisons of the individual machine learning models with the ARIMA algorithm, a large part of the applications indicate the superiority of the former based on the metrics used. However, there were a subset of studies in which ARIMA demonstrated higher predictive accuracy. We will refer to these studies in the rest of the present chapter in order to practically evaluate the performance of the ARIMA against the machine learning models and to uncover the circumstances (either dataset or model-dependent) under which the statistical approach exhibits superior performance in the task of time-series forecasting. ARIMA over SVM Models  
In the case of SVM algorithms, in the work of [PERSON] et al. [24] on drought prediction, the ARIMA algorithm had clearly better prediction performance based on various metrics, compared with the selected WNN and SVM models (Section 3.1.4). According to the authors of this paper, WNN and SVM machine learning models are not always superior to \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Article** & **Algorithms** & **Metrics** & **Dataset** \\ \hline [PERSON] et al. [4] & ARIMA/ANN & MSE & variety \\  & & MAD & \\ \hline  & ARIMA/FFNN & RMSE & bitcoin price \\ [PERSON] et al. [44] & ARIMA/CNN & MAPE & \\  & ARIMA/LSTM & & \\  & ARIMA/SVR & & \\ \hline [PERSON] et al. [57] & ARIMA/RF & NMAE & wind power \\  & ARIMA/BCART & & \\ \hline [PERSON] et al. [58] & ARIMA/NARNN & RMSE & COVID-19 cases \\ \hline [PERSON] et al. [5] & ARIMA/SVM & MAPE & short-term load forecasting \\  & & RMSE & forecasting \\ \hline [PERSON] et al. [59] & NN/ARIMA & MSE & network-wide \\  & MSVR/ARIMA & MAPE & traffic \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Summary of studies comparing ARIMA and Hybrid Models in time series forecasting. traditional ARIMA models in drought prediction. Different forecasting methods can be used for different geographic regions, and it would be subsequently advised for the data characteristics to be investigated in order to select the appropriate forecasting model. In the case of individual deep learning models vs. ARIMA, by introducing LSTM networks and the property of memory in the forecasting process, these models gain a great advantage over classical statistical forecasting methods, and this is shown by their dominance over ARIMA in the relevant literature. However, there are exceptions to this rule, which we will refer to below. In the work of [PERSON] et al. (2018) on stock index forecasting, the LSTM and XGBoost algorithms gave better forecasting results than ARIMA for all but two data sets, whose data values were significantly lower than the rest (Paragraph \"Financial Data\"). This fact probably indicates an advantage of statistical methods when the data is characterized by a limited range of values. ARIMA methods prevail over deep learning algorithms in bitcoin price prediction applications in the works of [PERSON] et al. (2018) and [PERSON] et al. (2018), and this result may be due to several factors, as the chosen values of the model parameters and the total amount of data can affect the results of the analysis. The volume of data in the work of [PERSON] et al. is relatively small, and RNN models usually perform well on more voluminous datasets, as previous studies have shown (Paragraph \"Financial Data\"). Regarding this particular observation, it is worth mentioning the related work of [PERSON] et al.