Long-Run Price Convergence and Market Efficiency in Selected Selected Cryptocurrencies: A Cointegration and Vector Error Correction Model Approach

Abstract

This study investigates long-run price convergence and weak-form market efficiency among major cryptocurrencies using daily closing prices for Bitcoin (BTC), Ethereum (ETH), Binance Coin (BNB), Solana (SOL), and Ripple (XRP) from April 11, 2020 to August 30, 2025. Unit root tests (ADF, PP, and DF-GLS) indicate that all price series are non-stationary in levels but stationary in first differences, confirming that they are integrated of order one, I(1). Johansen cointegration tests provide evidence of one cointegrating relationship (r ≤ 1) at the 5% significance level (trace statistic = 72.10 > 69.82), indicating a shared long-run equilibrium among the five cryptocurrencies. A Vector Error Correction Model (VECM) with rank one reveals statistically significant error-correction coefficients for all assets, with adjustment speeds of α = 0.005 for BTC, 0.007 for ETH, 0.013 for BNB, 0.017 for SOL, and 0.008 for XRP, implying slow and heterogeneous convergence toward equilibrium. The cointegration spread is highly persistent, with an estimated autoregressive coefficient of ρ = 0.995, corresponding to a half-life of approximately 151 days. Weak-form market efficiency tests based on Ljung-Box statistics and AR(1) regressions indicate that BTC and XRP exhibit return behavior consistent with weak-form efficiency, while ETH, BNB, and SOL display statistically significant short-run predictability. Overall, the results suggest that major cryptocurrency markets are strongly integrated in the long run but exhibit partial weak-form efficiency, with limited long-horizon diversification benefits and slow equilibrium adjustment.