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Cycle Envelope

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In plain English

Two power laws this time. A red line is drawn through confirmed cycle highs. A green line is drawn through confirmed cycle lows. Price usually lives in the envelope between them.

The lower pane flattens that envelope: 0 is the green line, 100 is the red line. Low teens means sitting on historically cheap cycle lows. High 90s means tagging historically expensive cycle highs.

Math and metrics

Daily USD closes. t = days since 2009-01-03. Cycle highs: ATH prints that later washed ≥55% and are ≥500 days apart. Troughs: min after each peak, only after a 2× bounce. A live wash that has not bounced 2× is scored against the green line, not refit into it.

log P = a + n log t on confirmed peaks → top; same on troughs → bottom. OLS on every close → fair.

osc = 100·(log P − log bottom) / (log top − log bottom). SMA_365 of osc mapped back to $ on the envelope.

Walk-forward “OOS inside envelope” = next-year weekly containment of the envelope frozen at each year-end from 2016.