D S Alekseev (Bauman Moscow State Technical University) :
Articles:
Oblakova T. V. (Bauman Moscow State Technical University), Alekseev D. S. (Bauman Moscow State Technical University)
doi: 10.18698/2309-3684-2022-4-4862
The work summarizes the results obtained in the course of the implementation of Bachelor's final qualifying work and is devoted to the methods of simulating and applying the fractional Brownian motion in the problems of time series analysis. Software modules have been implemented to generate trajectories of fractal Brownian motion using the methods of stochastic representation, Cholesky decomposition and Davis-Hart. Algorithms vere compared in terms of their complexity and the quality of the resulting trajectories. The Hurst exponent was estimated by the Minkowski and R/S analysis methods. An approximation of time series by fractal Brownian motion using a power function is proposed and implemented for the subsequent application of a linear prediction algorithm based on the normal correlation theorem. It has been established that with the help of the presented approximation it is possible to achieve a satisfactory forecast of the exchange rate for several values ahead.
Облакова Т.В., Алексеев Д.С. Сравнительный анализ методов моделирования и прогнозирования временных рядов на основе теории фрактального броуновского движения. Математическое моделирование и численные методы, 2022, № 4, с. 48–62
519.2 Investigation of time series forecasting quality using C++ implementation of AT-LSTM model
Oblakova T. V. (Bauman Moscow State Technical University), Alekseev D. S. (Bauman Moscow State Technical University)
doi: 10.18698/2309-3684-2025-1-8091
The implementation of recurrent neural network AT-LSTM (Attention based Long Short Term Memory) in C++ programming language is considered. This model was developed to reduce the training and inference times. The paper presents the architecture of this neural network and working examples, also describes the training procedure and results estimation. In the research work, calculations were carried out to estimate the performance of the AT-LSTM neural network for training and forward passes in comparison with the Python implementation. The performance analysis included the training time and the running time estimations of the neural network with the same length of input data but different values of hyperparameters. The calculations showed that it is possible to significantly decrease the training time, reduce the prediction error and maintain the high quality of the prediction results when using the C++ programming language implementation. In order to estimate the applicability of the considered AT-LSTM implementation in real cases, the precision of financial time series forecasting was analysed. USD/RUB and EUR/RUB currency rates, as well as Apple (AAPL) and Microsoft (MSFT) share prices were chosen as the objects of current research. The results showed that the obtained model is highly effective for time series forecasting and can be successfully applied in real cases. Finally, based on the experiments and analyses, it was concluded that the considered implementation of AT-LSTM in C++ allows for fast and high-quality training of the model for further time series forecasting.
Облакова Т.В., Алексеев Д.С. Исследование качества прогнозирования временных рядов с помощью реализации модели AT-LSTM на C++. Математическое моделирование и численные методы, 2025, № 1, с. 80–91.