Comparative analysis of cryptocurrency prices with Neural ODE deep learning method and time series models

This study aims to perform price forecasting by utilizing various artificial intelligence prediction algorithms and traditional econometric models, taking into account the high volatility and chaotic structure of cryptocurrency markets, and to identify the most successful model. In this context, daily time series data of Bitcoin, Ethereum and Ripple cryptocurrencies for the period 2019-2024 were used. In the research; price forecasts were made by using traditional econometric methods; ARIMA and GARCH models, as well as modern artificial intelligence techniques such as LSTM, Bi-LSTM and Neural ODEs. In addition, the chaotic structure of the data set was tested by means of the Lyapunov exponent, creating a scientific basis for model selection. This methodological approach increases the originality and comprehensiveness of the study and aims to base the model selection on the dynamic properties of the data structure. The analysis findings revealed that artificial intelligence-based forecasting models exhibit superior performance in predicting cryptocurrency markets compared to traditional econometric models. In addition, the Neural ODE model, which is a relatively new approach in the literature and has been used in a limited number of studies, has been extensively applied in this study to predict cryptocurrency prices and has achieved the highest prediction accuracy among all compared methods. Neural ODE's capacity to represent the continuous nature of the time series and its ability to deal with chaotic data structures has provided this model with a significant methodological advantage in highly volatile cryptocurrency markets. After Neural ODE, it was seen that the model that provided the highest success was LSTM, which is also a deep learning architecture. This situation is; It clearly shows the usability and effectiveness of artificial intelligence techniques in dynamic and unpredictable areas such as the cryptocurrency market. This study, which examines the Neural ODE model in detail, offers an original and pioneering contribution to the literature in terms of both methodological innovation and practical success; in this respect, it stands out as one of the first comprehensive analyses on the subject. In addition, it is an important resource that can guide future academic research by revealing the potential of new generation artificial intelligence techniques in the field of financial time series modeling.