RESEARCH
The full math, with references.
Formal research notes underneath the Hedgicore methodology paper. Cointegration, OU processes, hedge-ratio estimation, the backtest-validation toolkit and the substrate considerations specific to crypto perpetuals. Citations are to original peer-reviewed work.
If you want the shorter, principle-level treatment, read the methodology paper first. The research notes are for readers who want the equations.
Pairs Trading Implementation. Hedge Ratio Estimation, Trading Rules and Backtesting.
Six hedge-ratio estimators, the closed-form Bertram optimal-stopping system, the four conventional responses to the hedge-ratio update continuity problem, and the formal backtest-validation toolkit.
Companion to the technical guide. Six hedge-ratio estimators (OLS, TLS, Johansen, Box-Tiao, Kalman, half-life-minimisation, ADF-optimisation). Trading rule construction from heuristic thresholds through Bertram closed-form optimal stopping and stochastic control. The hedge-ratio update continuity problem and four conventional responses. Backtest validation: walk-forward, block bootstrap, PSR, DSR, PBO, transaction-cost realism, survivorship and multiple-testing correction. 22 references.
Statistical Arbitrage. A Technical Guide.
Stationarity, cointegration, VECM, OU processes, the five method families and crypto-specific substrate considerations.
Formal mathematical treatment of statistical arbitrage. Stationarity, integration order, cointegration, the Granger Representation Theorem, VECM, multivariate Johansen, OU processes, half-life and Hurst exponent. The five academic method families. Crypto-perpetual substrate. 51 references to original peer-reviewed work.