On Bitcoin cycles

Abstract

This paper tests whether Bitcoin’s four-year cycle persists in monthlyreturn dynamics after the asset’s recent institutionalization. Weestimate harmonic Fourier regressions with 48- and 24-month componentsand allow the cycle coefficients to shift after a May 2023 structuralbreakpoint. We compare an unconditional model with a macro-conditionedspecification that includes S\&P 500 and U.S. Dollar Index returns.The unconditional results indicate a significant post-break changeand a sharp reduction in cyclical amplitude. However, after controllingfor broader market and liquidity conditions, the residual four-yearcomponent loses statistical significance. The evidence suggests thatBitcoin’s historical halving-related rhythm has weakened and thatits return dynamics are increasingly linked to global macro-financialconditions.