Quantifying Cryptocurrency Unpredictability: A Comprehensive Study of Complexity and Forecasting
Francesco Puoti, Fabrizio Pittorino, Manuel Roveri
TL;DR
This paper investigates the univariate predictability of USD crypto time-series by combining complexity analysis (Permutation Entropy, CH-plane, and Jensen-Shannon complexity) with a wide range of forecasting models, spanning naive, statistical, ML, and DL methods. Through data on five major cryptocurrencies (LTC, BNB, BTC, ETH, XRP) from 2020–07–03 to 2023–12–21 and a rolling-window backtesting framework, the study demonstrates that crypto price dynamics exhibit Brownian-like noise characteristics across horizons, with high entropy and low complexity. Intriguingly, simpler statistical models often outperform more complex ML/DL approaches, and several advanced models do not provide clear predictive gains over naive benchmarks. The findings challenge the assumption that higher model complexity yields better forecasts in this domain, and they suggest that incorporating exogenous covariates could unlock improvements, guiding future research toward covariate-rich, context-aware crypto forecasting.
Abstract
This paper offers a thorough examination of the univariate predictability in cryptocurrency time-series. By exploiting a combination of complexity measure and model predictions we explore the cryptocurrencies time-series forecasting task focusing on the exchange rate in USD of Litecoin, Binance Coin, Bitcoin, Ethereum, and XRP. On one hand, to assess the complexity and the randomness of these time-series, a comparative analysis has been performed using Brownian and colored noises as a benchmark. The results obtained from the Complexity-Entropy causality plane and power density spectrum analysis reveal that cryptocurrency time-series exhibit characteristics closely resembling those of Brownian noise when analyzed in a univariate context. On the other hand, the application of a wide range of statistical, machine and deep learning models for time-series forecasting demonstrates the low predictability of cryptocurrencies. Notably, our analysis reveals that simpler models such as Naive models consistently outperform the more complex machine and deep learning ones in terms of forecasting accuracy across different forecast horizons and time windows. The combined study of complexity and forecasting accuracies highlights the difficulty of predicting the cryptocurrency market. These findings provide valuable insights into the inherent characteristics of the cryptocurrency data and highlight the need to reassess the challenges associated with predicting cryptocurrency's price movements.