Memory Persistence in Minute Frequency Cryptocurrencies: Analysis Based on Hurst-Exponent and LSTM Brownian Diffusion Network

Ascertaining and characterizing trends in high and middle-frequency data periods is crucial and demanding. We studied every minute of available cryptocurrency data on Yahoo over a first period of three weeks, from May 15, 2023, to June 2, 2023, and a second period from May 19, 2024, to June 7, 2024. Cryptocurrencies were chosen since they have lower exchange volumes compared to other financial products. (1) Our analysis resulted in six groups per period of cryptocurrency time series accumulated returns through clustering. (2) We compute the Hurst exponent and its temporal evolution using a sliding window technique to measure the memory autoregressive trends in the time series. (3) Based on our findings, we employed the LSTM model on one of the components of each cluster to make a forecast and compare it with actual data. (4) Our research revealed that if the average Hurst exponent of a time series deviates from the stochastic regime, then the series is suitable for forecasting using the LSTM method. (5) We also developed an LSTM-Bm model that captures the time series’ stochastic nature to describe the forecasting diffusion. (6) We empirically show an inverse relationship between the Hurts exponent and the relative error of memory-based forecasting.