## 3 Machine Learning Models
### Deep Learning Models
#### 3.3.3 Long-Short Term Memory Networks (LSTM)
This paper concludes that although the accuracy metrics indicate a satisfactory performance of the ARIMA algorithm, the ARIMA prediction based on the error metrics is much less satisfactory than the LSTM model. The authors of the paper emphasize that the ARIMA model was able to achieve a correct prediction due to the upward trend of the bitcoin price time series and that if the trend was downward, ARIMA could not have given a correct prediction. The work of [PERSON] et al. [47] resides in the financial sector but concerns itself with the prediction of the budget consumed by a government organization. Furthermore, the superiority of LSTMs is evident over ARIMA due to their increased ability in identifying non-linear structures in financial time series. Utilities  
The work of [PERSON] et al. [48] compares the ARIMA technique with Prophet, a scalable forecasting tool available from Meta based on a generalized additive model, and deep learning models LSTM and CNN (convolutional neural networks). The study regards data from three wholesale alimentary product prices, and the parameters of the ARIMA approach to the forecasting problem correspond to each of the datasets. The findings showed that while the Prophet model is fast to train and requires no data preprocessing, it is not able to come close to the performance of the other models, and its use is recommended only when simplicity and speed of prediction are the main requirements of the analysis. In contrast, ARIMA models and LSTM neural networks perform similarly for the forecasting task under consideration, while the combination of CNN and LSTM achieves the best overall accuracy but requires more time to tune the hyperparameters. Therefore, when fairly accurate forecasts and short forecast extraction times are required in a particular multivariate data set, the paper suggests the use of simple LSTM models over univariate ARIMA models. Finally, the work of [PERSON] et al. [49] deals with the prediction of oil production time series, consisting of data on fluctuations in the operations of a specific well and its reservoirs. Three algorithms are studied to address the limitations of traditional production forecasting: the ARIMA method, the LSTM network, and the Prophet forecasting tool. The advantages of machine learning models are workflow simplicity, fast and reliable prediction for a typical declining production curve. An important feature of the Prophet model is the ability it provides to record winter fluctuations in production, which can, by alerting the operator, prevent potential failures. The application of ARIMA, LSTM, and Prophet methods to 65 wells in the DJ basin shows that ARIMA and LSTM techniques perform better than the Prophet model, possibly because not all oil production data includes seasonal variations. In addition, wells in nearby reservoirs can be studied using the same parameter values in ARIMA and LSTM models to predict oil production using a transferred learning framework. In particular, ARIMA is observed to be effective in predicting the oil production rate of wells across the DJ basin. Although the majority of works dealing with the comparison of classical statistical analysis methods with machine and deep learning methods in time series forecasting are based on applications in the financial sector, we will also refer to works related to the fields of medical care, the environment, and technology.