The Bitcoin Polar Pricing Model: Cycles, Prices, and Predictability

Abstract

We develop a Bitcoin Polar Pricing Model that transforms Bitcoin prices into polar coordinates to identify, price, and forecast cyclical dynamics. Rather than imposing the four-year halving cycle, we estimate it endogenously: three independent methods converge on 3.86 years, and Bitcoin sits closer to the 1,461-day halving benchmark than Ethereum or the S&P 500 placebos under every method. The model explains 94% of Bitcoin's log-price variation, with significant within-cycle Fourier structure. Apparent predictability rises with horizon, a pattern we interpret cautiously given known overlappingwindow biases. Collectively, the polar pricing model offers a legitimate, economically grounded framework for pricing Bitcoin.