Adaptive Quantile Calibration of Daily and Weekly Cycle-Low Forecasts in Bitcoin, S&P 500 Futures, and Gold

Abstract

Background. Market-cycle forecasts are vulnerable to hindsight because a low becomes identifiable only after subsequent price confirmation.

Objective. This study evaluated whether an adaptive, confirmation-aware interval could attain at least 80% chronological forecast precision for daily cycle lows (DCLs) and weekly cycle lows (WCLs) in Bitcoin, S&P 500 futures, and gold.

Methods. The Adaptive Quantile-Calibrated Cycle Window used only the latest 20 completed cycles. Its lower endpoint was the empirical 10th percentile of prior low-to-low durations, and its upper endpoint was the 90th percentile of prior-low-to-next-confirmation durations. Forecasts originating from 1 January 2021 through 14 July 2026 were evaluated sequentially, and the retrospective protocol was externally preregistered.

Results. Fixed clocks achieved 70.9% DCL precision and 55.6% WCL precision. The adaptive interval achieved 109/127 DCL hits (85.8%; 95% CI 78.7%–90.8%) and 27/27 WCL hits (100.0%; 95% CI 87.5%–100.0%). Mean window width increased from 14.7 to 32.8 days for DCL and from 4.0 to 11.7 weeks for WCL. A wider 5th–95th percentile band produced 93.7% DCL precision with a 95% lower confidence bound of 88.1%.

Conclusion. Adaptive interval calibration exceeded the 80% point target, but the gain depended on materially wider windows and a small WCL sample; prospective replication remains necessary.