Pricing trends of cryptocurrency: an empirical analysis of Bitcoin and Ethereum, 2020–2025

Abstract

A current, urgent problem is whether the price behavior pattern of significant quantities of digital assets reflects a single direction trend line or multiple phases that exhibit different structures, adjusted inter-asset relationship differences, and changes in management systems, given the growing importance of digital assets in investment portfolios and collateral holdings, exchange-traded funds (ETFs), new forms of financial activities, and system risks over the period from 2020 through 2025. Because of this period’s post-pandemic recovery, speculative overextension, sharp decline, stabilization, and the re-entry of large-scale institutions into practice, these changes in prices are more clearly identified under such a context. Empirically, this study integrates descriptive statistics, rolling volatility analysis, augmented Dickey–Fuller’s unit-root test, segmented trend regression model with structural breaks, and vector autoregression (VAR) for return interactions. Based on these bases, both Bitcoin and Ethereum have demonstrated a relatively strong direction of continuous appreciation, together with quite considerable regime-specific instability. The log-price series is non-stationary, but the daily return series is stationary; so a level model is appropriate for medium-term trend analysis, and returns-based models can be applied more flexibly at shorter timespans. The segmented trend-regression analysis shows that close to peaks, such as those that occurred in 2021 for a long period, the 2022 correction, and the resumption of investment in 2024, are relatively distinct from the overall linear change pattern across all time periods. Both Bitcoin and Ethereum display pronounced contemporaneous co-movement, but they show no substantial lags via VAR or Granger causality tests conducted in the context of time-varying parameters. This study employs an integrated empirical research approach based on various perspectives to explore the long-term structural adjustment and near-instantaneous cross-market relationship dynamics, as well as regulatory mechanisms within a systemic context.