Backtest

The test that chose the model

Before any coin was published, four models were run on its own history and compared on data they had not seen. This page is the whole test, numbers included, so nobody has to take "it passed" on faith.

What was tested

M0. Lognormal, no drift, sigma = standard deviation of the last 30 daily log returns, annualised with sqrt(365), scaled by sqrt(h/365).
M1. Same as M0 but sigma = exponentially weighted moving average of squared daily log returns, lambda 0.94 (RiskMetrics), annualised. The official model, version M1.0.
M2. Same lognormal, sigma = Deribit DVOL implied-volatility index of the day. Bitcoin and Ethereum only (Deribit publishes no DVOL for the others).
M3. Empirical: the percentiles of the last 365 days of h-day log returns, centered on today's price. No distribution assumed.

All four forecast the same thing: the 5th, 10th, 25th, 50th, 75th, 90th and 95th percentiles of the close 1, 7 and 30 days ahead, with the median fixed at today's price (no model tries to guess direction). They are graded with the pinball loss averaged over the seven percentiles, as a share of the price (lower is better), and by how often the close landed inside the 10th–90th range (target 80%).

Periods and rule

Development: 2021-04-01 to 2023-12-31. Holdout: 2024-01-01 to 2026-09-25, looked at once. Data: Binance daily closes at 00:00 UTC; Deribit DVOL for M2.

Pass rule, written before running: A model passes for a coin if it beats M0 on pinball loss in the development period AND in the holdout in at least 2 of the 3 horizons. For coins added later (H80, Oct 24, 2026) the holdout 80% range must also cover between 70% and 90% of closes at 1 and 7 days. The holdout was looked at once.

Declared Oct 7, 2026 for Bitcoin, Ethereum and Solana; the four coins added on Oct 24, 2026 were tested with the same models, periods and rule. Coins that failed the test: none so far. If one fails, it is listed here and does not get a page.

Result

M1 beat M0 in development and holdout in every horizon for six coins and in 2 of 3 for Solana. The margins are small: a well-tuned EWMA draws ranges of the right width; it is not a crystal ball. M2 and M3 won some horizons in the holdout, M3 especially at 30 days; they keep running in the shadow and can take over by the published rule. Pinball in % of price, lower is better; coverage of the 80% range in the holdout, target 80%.

Bitcoin tested Oct 7, 2026 · passed · M1 won 3 of 3 horizons

Horizon	Period	M0	M1	M2	M3
1 day	development	0.706	0.703	0.712	0.702
1 day	holdout	0.552	0.549	0.546	0.548
7 days	development	1.950	1.948	1.965	1.907
7 days	holdout	1.507	1.493	1.472	1.448
30 days	development	4.334	4.289	4.220	4.200
30 days	holdout	3.573	3.562	3.417	3.429
1 day	coverage, holdout	82.2%	82.3%	86.7%	79.5%
7 days	coverage, holdout	79.5%	80.3%	86.5%	79.5%
30 days	coverage, holdout	76.0%	76.8%	79.4%	74.5%

Ethereum tested Oct 7, 2026 · passed · M1 won 3 of 3 horizons

Horizon	Period	M0	M1	M2	M3
1 day	development	0.903	0.896	0.893	0.907
1 day	holdout	0.794	0.790	0.781	0.786
7 days	development	2.401	2.399	2.377	2.358
7 days	holdout	2.247	2.233	2.158	2.169
30 days	development	5.089	5.067	5.054	5.154
30 days	holdout	5.301	5.287	5.152	5.377
1 day	coverage, holdout	83.0%	83.4%	85.0%	78.3%
7 days	coverage, holdout	79.0%	79.0%	81.1%	76.7%
30 days	coverage, holdout	70.4%	70.1%	71.4%	66.4%

Solana tested Oct 7, 2026 · passed · M1 won 2 of 3 horizons

Horizon	Period	M0	M1	M2	M3
1 day	development	1.396	1.377	—	1.388
1 day	holdout	0.928	0.922	—	0.925
7 days	development	4.177	4.124	—	4.005
7 days	holdout	2.469	2.473	—	2.411
30 days	development	12.643	12.349	—	11.745
30 days	holdout	5.575	5.491	—	5.121
1 day	coverage, holdout	81.1%	82.0%	—	82.6%
7 days	coverage, holdout	79.2%	79.2%	—	81.2%
30 days	coverage, holdout	76.2%	77.2%	—	84.7%

XRP tested Oct 24, 2026 · passed · M1 won 3 of 3 horizons

Horizon	Period	M0	M1	M2	M3
1 day	development	1.101	1.084	—	1.093
1 day	holdout	0.881	0.870	—	0.876
7 days	development	3.064	3.019	—	3.007
7 days	holdout	2.637	2.603	—	2.626
30 days	development	6.476	6.422	—	6.556
30 days	holdout	7.930	7.874	—	8.190
1 day	coverage, holdout	83.1%	83.5%	—	79.1%
7 days	coverage, holdout	81.1%	83.1%	—	79.4%
30 days	coverage, holdout	76.4%	77.2%	—	78.2%

Litecoin tested Oct 24, 2026 · passed · M1 won 3 of 3 horizons

Horizon	Period	M0	M1	M2	M3
1 day	development	1.025	1.016	—	1.013
1 day	holdout	0.810	0.808	—	0.814
7 days	development	2.672	2.655	—	2.612
7 days	holdout	2.094	2.089	—	2.092
30 days	development	4.967	4.878	—	4.782
30 days	holdout	4.409	4.361	—	4.230
1 day	coverage, holdout	82.7%	83.0%	—	80.3%
7 days	coverage, holdout	81.9%	82.8%	—	79.4%
30 days	coverage, holdout	79.6%	80.6%	—	73.8%

Dogecoin tested Oct 24, 2026 · passed · M1 won 3 of 3 horizons

Horizon	Period	M0	M1	M2	M3
1 day	development	1.260	1.243	—	1.300
1 day	holdout	1.039	1.036	—	1.054
7 days	development	4.195	4.151	—	4.375
7 days	holdout	3.054	3.047	—	3.052
30 days	development	10.411	10.259	—	12.018
30 days	holdout	8.365	8.335	—	8.401
1 day	coverage, holdout	82.6%	83.3%	—	79.7%
7 days	coverage, holdout	79.9%	80.9%	—	77.7%
30 days	coverage, holdout	74.0%	75.1%	—	76.8%

Hedera tested Oct 24, 2026 · passed · M1 won 3 of 3 horizons

Horizon	Period	M0	M1	M2	M3
1 day	development	1.149	1.132	—	1.153
1 day	holdout	1.096	1.086	—	1.088
7 days	development	2.762	2.748	—	2.705
7 days	holdout	3.327	3.306	—	3.317
30 days	development	6.280	6.184	—	6.525
30 days	holdout	10.474	10.397	—	10.858
1 day	coverage, holdout	81.8%	81.8%	—	80.0%
7 days	coverage, holdout	79.7%	81.0%	—	77.4%
30 days	coverage, holdout	77.0%	80.7%	—	74.7%

Bold is the best pinball in the row. Forecasts at 7 and 30 days overlap day to day, so the effective sample is smaller than the number of days. Solana and the four coins added later have no M2: Deribit publishes no implied volatility for them. The live record of all four models, coin by coin, is on each coin's page under "The models in the shadow".