Discrete and Continuous Models and Applied Computational ScienceDiscrete and Continuous Models and Applied Computational Science2658-46702658-7149Peoples' Friendship University of Russia2613810.22363/2658-4670-2021-29-1-22-35Research ArticleStudy of the impact of the COVID-19 pandemic on international air transportationShchetininEugeny Yu.<p>Doctor of Physical and Mathematical Sciences, Lecturer of Department of Mathematics</p>riviera-molto@mail.ruFinancial University under the Government of Russian Federation30032021291223530032021Copyright © 2021, Shchetinin E.Y.2021<p style="text-align: justify;">Time Series Forecasting has always been a very important area of research in many domains because many different types of data are stored as time series. Given the growing availability of data and computing power in the recent years, Deep Learning has become a fundamental part of the new generation of Time Series Forecasting models, obtaining excellent results.As different time series problems are studied in many different fields, a large number of new architectures have been developed in recent years. This has also been simplified by the growing availability of open source frameworks, which make the development of new custom network components easier and faster.In this paper three different Deep Learning Architecture for Time Series Forecasting are presented: Recurrent Neural Networks (RNNs), that are the most classical and used architecture for Time Series Forecasting problems; Long Short-Term Memory (LSTM), that are an evolution of RNNs developed in order to overcome the vanishing gradient problem; Gated Recurrent Unit (GRU), that are another evolution of RNNs, similar to LSTM.The article is devoted to modeling and forecasting the cost of international air transportation in a pandemic using deep learning methods. The author builds time series models of the American Airlines (AAL) stock prices for a selected period using LSTM, GRU, RNN recurrent neural networks models and compare the accuracy forecast results.</p>neural networksfinancial forecastingdeep learninginternational air travelнейронные сетифинансовое прогнозированиеглубокое обучениемеждународные авиаперевозки[J. D. A. Hamilton, The time series analysis. Princeton New Jersey: University Press, 1994.][C. Brooks, Introductory econometrics for finance. Cambridge: Cambridge University Press, 2019.][“American Airlines Group Inc. (AAL),” URL: https://finance.yahoo. com/quote/AAL/. Availabel: 2020-11-25, 2020.][E. Y. Shchetinin, “On a structural approach to managing a company with high volatility of indicators [K analizu effektivnosti biznesa v usloviyah vysokoj izmenchivosti ego finansovyh aktivov],” Finansy i kredit, vol. 14, no. 218, pp. 39-41, 2006, [in Russian].][J. Vander Plas, Python Data Science Handbook. Sebastopol, CA: O’Reilly Media, 2016.][W. Richert and L. P. Coelho, Building Machine Learning Systems with Python. Birmingham: Packt, 2013.][C. Bishop, Pattern recognition and machine learning. Berlin, Germany: Springer-Verlag, 2006.][E. Y. Shchetinin, “Modeling the energy consumption of smart buildings using artificial intelligence,” in CEUR Workshop Proceedings, vol. 2407, 2019, pp. 130-140.][M. Mudelsee, “Trend analysis of climate time series: A review of methods,” Earth-Science Reviews, vol. 190, pp. 310-322, 2019. DOI: 10.1016/ j.earscirev.2018.12.005.][C. Chen, J. Twycross, and J. M. Garibaldi, “A new accuracy measure based on bounded relative error for time series forecasting,” PLOS ONE, vol. 12, no. 3, pp. 1-23, Mar. 2017. DOI: 10. 1371 / journal. pone. 0174202.][R. J. Hyndman and G. Athanasopoulos, Forecasting: principles and practice. Melbourne, Australia: OTexts, 2018.][A. Ghaderi, B. M. Sanandaji, and F. Ghaderi. “Deep forecast: deep learning-based spatio-temporal forecasting.” arXiv: 1707.08110 [cs.LG]. (2017).][S. B. Taieb, A. Sorjamaa, and G. Bontempi, “Multiple-output modeling for multi-step-ahead time series forecasting,” Neurocomput, vol. 73, no. 10, pp. 1950-1957, 2010. DOI: 10.1016/j.neucom.2009.11.030.][R. Sen, H.-F. Yu, and I. S. Dhillon, “Think globally, act locally: a deep neural network approach to high-dimensional time series forecasting,” in Advances in neural information processing systems, H. Wallach, H. Larochelle, A. Beygelzimer, F. d’Alché-Buc, E. Fox, and R. Garnett, Eds., vol. 32, Curran Associates, Inc., 2019.][“Keras,” URL: https://www.keras.io. Availabel: 2020-11-25, 2020.][I. Goodfellow, Y. Bengio, and A. Courville, Deep learning. Cambridge: The MIT Press, 2016.][S. Galeshchuk and S. Mukherjee, “Deep networks for predicting direction of change in foreign exchange rates,” Intelligent Systems in Accounting, Finance and Management, vol. 24, no. 4, pp. 100-110, 2017. DOI: 10. 1002/isaf.1404.]