diff --git a/docs/experiments/2026-11-09-paxg-last-two-digits.jsonl b/docs/experiments/2026-11-09-paxg-last-two-digits.jsonl new file mode 100644 index 00000000..96698978 --- /dev/null +++ b/docs/experiments/2026-11-09-paxg-last-two-digits.jsonl @@ -0,0 +1,4 @@ +{"row": "arm", "arm": "usd_dollars", "n_windows": 3275, "first_ts": 1746734400, "last_ts": 1794168000, "up_rate": "0.5044274809160305343511450382", "chi_square": "118.669167", "chi_null_median": "98.258133", "p_chi": "0.096952", "n_train": 1965, "n_test": 1310, "test_up_rate": "0.4618320610687022900763358779", "oos_hit_rate": "0.489313", "oos_null_median": "0.487023", "oos_null_p95": "0.509160", "p_oos": "0.452274", "n_up_calls": 882, "mean_gross_up_call": "-0.000090", "mean_net_up_call": "-0.018008", "median_abs_4h_move": "0.001953", "shows_dependence": false} +{"row": "arm", "arm": "usd_cents", "n_windows": 3275, "first_ts": 1746734400, "last_ts": 1794168000, "up_rate": "0.5044274809160305343511450382", "chi_square": "108.994413", "chi_null_median": "98.269937", "p_chi": "0.233383", "n_train": 1965, "n_test": 1310, "test_up_rate": "0.4618320610687022900763358779", "oos_hit_rate": "0.492366", "oos_null_median": "0.487786", "oos_null_p95": "0.512977", "p_oos": "0.394803", "n_up_calls": 878, "mean_gross_up_call": "-0.000149", "mean_net_up_call": "-0.018065", "median_abs_4h_move": "0.001953", "shows_dependence": false} +{"row": "arm", "arm": "usdt_dollars", "n_windows": 10082, "first_ts": 1626652800, "last_ts": 1784318400, "up_rate": "0.5075381868676849831382662170", "chi_square": "89.896793", "chi_null_median": "98.149495", "p_chi": "0.737131", "n_train": 6049, "n_test": 4033, "test_up_rate": "0.5283907760971981155467394000", "oos_hit_rate": "0.489214", "oos_null_median": "0.495909", "oos_null_p95": "0.509298", "p_oos": "0.797101", "n_up_calls": 1529, "mean_gross_up_call": "0.000100", "mean_net_up_call": "-0.017821", "median_abs_4h_move": "0.001654", "shows_dependence": false} +{"row": "verdict", "verdict": "not supported"} diff --git a/docs/experiments/2026-11-09-paxg-last-two-digits.md b/docs/experiments/2026-11-09-paxg-last-two-digits.md new file mode 100644 index 00000000..42fce44a --- /dev/null +++ b/docs/experiments/2026-11-09-paxg-last-two-digits.md @@ -0,0 +1,50 @@ +# Do the last two digits of PAXG's price predict the next four hours? — No + +**Pre-registered.** The driver `2026-11-09-paxg-last-two-digits.py` was committed and pushed +(30dbe5b) before it ran on real data. Its docstring sets out the method and the decision rule. +Not a promotion decision: three `diagnostic_only` rows in the trials ledger. + +## The claim +An outside observer claimed that the last two digits of PAXG's price on the starting candle +predict whether it rises or falls over the next four hours. No rule came with the claim. The +test therefore asks the question any such rule depends on: do the digits carry any information +about the sign of the 4-hour move? Each test can find any mapping from digits to direction, +including one fitted to the data, so a null here also rules out every specific rule. + +## Result + +| arm | windows | in-sample chi-square p | out-of-sample hit rate | null median / p95 | OOS p | shows dependence | +| :--- | ---: | ---: | ---: | ---: | ---: | :---: | +| Coinbase, dollar digits | 3,275 | 0.097 | 48.9% | 48.7% / 50.9% | 0.45 | no | +| Coinbase, cents | 3,275 | 0.233 | 49.2% | 48.8% / 51.3% | 0.39 | no | +| Binance 2021–26, dollar digits | 10,082 | 0.737 | 48.9% | 49.6% / 50.9% | 0.80 | no | + +Bonferroni alpha is 0.0167. **Verdict: not supported.** No arm comes close: on all three, the +map learned from the first 60% of windows did no better on the last 40% than a map learned +from shuffled outcomes. + +## Economics, even if the claim had been true +- The median absolute 4-hour move is **0.20%** on Coinbase and 0.17% on Binance. +- The Advanced Trade round trip at 0.9% taker per leg costs **1.8%**, about nine times the + typical move. +- Buying on every "up" call in the test set: mean gross return per call was −0.009%, +0.015% + or +0.010% depending on the arm. Mean net return was **−1.80%** on all three. + +A perfect directional call on a typical window earns about 0.2% before costs, so no +direction-prediction edge on this horizon can pay keel's fees. + +## Why one would expect this +For a price in the thousands, the last two digits are the fastest-cycling part of the number. +A 0.2% move on a $4,000 price is $8 in the dollar digits, so 4-hour volatility wraps them +around many times over. They are close to uniform noise. The best-known exception is clustering +near round numbers (support and resistance at …00). Any such effect would sit inside a 100-cell +test like this one and would have to be large to matter. Eyeballed patterns in digits are a +textbook case of seeing structure in a small sample. Here, 100 cells with about 33 windows +each will always produce a few digits that look like they "work" by chance. + +## Limits +- The test has power against a broad dependence. A narrow rule, such as one digit or a + handful, at a few points of edge, could hide inside 100 cells. Testing such a rule needs the + friend's exact mapping, stated in advance and scored only on windows after it was written. +- The Binance and Coinbase samples overlap from 2025-05 to 2026-07. The replication is not + fully independent there. diff --git a/docs/experiments/2026-11-09-paxg-last-two-digits.py b/docs/experiments/2026-11-09-paxg-last-two-digits.py new file mode 100644 index 00000000..f9bb6287 --- /dev/null +++ b/docs/experiments/2026-11-09-paxg-last-two-digits.py @@ -0,0 +1,275 @@ +#!/usr/bin/env python +"""Do the last two digits of PAXG's price at a 4-hour window's open predict that window's direction? + +**Pre-registered.** This docstring and the code below were committed and pushed before the +first run. Nothing here was chosen after seeing a result. + +## The claim under test +An outside observer says the last two digits of PAXG's price on the "starting candle" predict +whether PAXG rises or falls over the next four hours. The claim came without a rule: which +digits map to "up" was not stated. So this tests the claim in its weakest form, the form any +specific rule would need to be true: **the two digits carry information about the sign of the +next 4-hour move.** If no mapping from digits to direction works out of sample, no particular +rule does either. + +## Data (fixed before the run) +- **Primary, Coinbase `PAXG-USD`** (the venue keel trades), `ONE_HOUR` candles from + `~/keel/keel.db`, every bar up to `END_TS` (2026-11-09 00:00 UTC). About 18 months. +- **Replication, Binance `PAXG-USDT`**, `ONE_HOUR`, the same cache, up to its last bar + (2026-07-18). About five years. Binance quoted PAXG in whole dollars for much of 2022-2023, so + the cents are 00 for that stretch. That arm therefore uses the dollar digits only. + +## Windows +Non-overlapping 4-hour windows aligned to UTC (00, 04, 08, 12, 16, 20). A window counts only +if all four hourly bars are present. Start price = the open of the first hour; end price = the +close of the fourth. Outcome = up if end > start, down if end < start. Flat windows are dropped. + +## Two meanings of "last two digits", three arms +- `usd_dollars`: Coinbase, `floor(start) mod 100` (4673.49 -> 73). +- `usd_cents`: Coinbase, the cents (4673.49 -> 49). +- `usdt_dollars`: Binance, `floor(start) mod 100`. This is the replication arm. + +## Tests, per arm +1. **In-sample dependence.** The chi-square statistic of the 100 x 2 table (digit x up/down), + with its p-value taken from 2,000 permutations of the outcomes (seed 1109), not from the + asymptotic distribution, because 100 cells leave some of them thin. +2. **Out of sample (the decisive test).** Split chronologically: the first 60% of windows + train, the last 40% test. On train, each digit is mapped to its majority direction (a tied + or unseen digit takes the train set's overall majority). Score the hit rate on test. The + null: shuffle the train outcomes among train windows, refit, rescore, 2,000 times (seed + 1109). That keeps the base rate, so a trending market cannot pass for skill. + p = (1 + #null >= observed) / 2001. +3. **Economics, reported and not tested.** keel's spot account can't short, so the only + tradeable call is "up". On the test set, the gross and net 4-hour return of buying at the + start price whenever the map says "up". Net is after a 0.9% taker fee on each leg + (`keel-advanced-trade-is-not-fee-free`). Also reported: the median absolute 4-hour move on the + full sample, set against the 1.8% round trip. + +## Decision rule (fixed) +Three arms means a Bonferroni alpha of 0.05 / 3 = 0.0167. +- An arm **shows dependence** only if both permutation p-values are below 0.0167. +- The claim is **supported** only if a Coinbase arm shows dependence, and, for a dollar-digit + effect, `usdt_dollars` shows it too. Otherwise it is **not supported**. +- Even a supported claim is **tradeable** only if the test-set mean net return per "up" call + is above zero. + +## Ledger +Each arm is appended to the trials ledger (`--ledger`) as `kind="ablation"`, +`provenance="a_priori"`, `decision="diagnostic_only"`. `per_trade_pnl` holds the arm's +test-set net returns per "up" call, as fractions of notional, not dollars. + +## Safety +Read-only. The cache is opened `mode=ro`. The only writes are `--out`, `--ledger` and stdout. +""" + +from __future__ import annotations + +import argparse +import json +import random +import sqlite3 +import statistics +from decimal import Decimal +from pathlib import Path +from typing import Any + +from keel.research.ledger import append_trial + +SESSION = "paxg-last-two-digits-2026-11-09" +END_TS = 1794182400 # 2026-11-09 00:00 UTC +WINDOW_S = 4 * 3600 +HOUR_S = 3600 +TRAIN_FRACTION = Decimal("0.6") +N_PERM = 2000 +SEED = 1109 +ALPHA = Decimal("0.05") / 3 +TAKER = Decimal("0.009") + +ARMS = ( + ("usd_dollars", "PAXG-USD", "dollars"), + ("usd_cents", "PAXG-USD", "cents"), + ("usdt_dollars", "PAXG-USDT", "dollars"), +) + + +def _hourly(db: str, product: str) -> dict[int, tuple[Decimal, Decimal]]: + conn = sqlite3.connect(f"file:{db}?mode=ro", uri=True) + rows = conn.execute( + "SELECT ts, o, c FROM candles WHERE product_id = ? AND granularity = 'ONE_HOUR' " + "AND ts < ? ORDER BY ts", + (product, END_TS), + ).fetchall() + conn.close() + return {int(ts): (Decimal(o), Decimal(c)) for ts, o, c in rows} + + +def windows(hourly: dict[int, tuple[Decimal, Decimal]]) -> list[tuple[int, Decimal, Decimal]]: + """`(start_ts, start_price, end_price)` per complete, non-flat, UTC-aligned 4-hour window.""" + out = [] + for ts in sorted(hourly): + if ts % WINDOW_S: + continue + hours = [ts + k * HOUR_S for k in range(4)] + if not all(h in hourly for h in hours): + continue + start, end = hourly[hours[0]][0], hourly[hours[-1]][1] + if end != start: + out.append((ts, start, end)) + return out + + +def digit(price: Decimal, kind: str) -> int: + if kind == "dollars": + return int(price) % 100 + return int(price * 100) % 100 + + +def chi_square(digits: list[int], ups: list[bool]) -> float: + n = len(ups) + p_up = sum(ups) / n + count = [0] * 100 + up = [0] * 100 + for d, u in zip(digits, ups, strict=True): + count[d] += 1 + up[d] += u + stat = 0.0 + for d in range(100): + if count[d] == 0: + continue + e_up = count[d] * p_up + e_dn = count[d] - e_up + stat += (up[d] - e_up) ** 2 / e_up + ((count[d] - up[d]) - e_dn) ** 2 / e_dn + return stat + + +def fit_map(digits: list[int], ups: list[bool]) -> list[bool]: + overall = sum(ups) * 2 > len(ups) + count = [0] * 100 + up = [0] * 100 + for d, u in zip(digits, ups, strict=True): + count[d] += 1 + up[d] += u + return [overall if up[d] * 2 == count[d] else up[d] * 2 > count[d] for d in range(100)] + + +def hit_rate(mapping: list[bool], digits: list[int], ups: list[bool]) -> float: + return sum(mapping[d] == u for d, u in zip(digits, ups, strict=True)) / len(ups) + + +def perm_p(observed: float, null: list[float]) -> Decimal: + return Decimal(1 + sum(x >= observed for x in null)) / Decimal(len(null) + 1) + + +def run_arm(arm: str, wins: list[tuple[int, Decimal, Decimal]], kind: str) -> dict[str, Any]: + rng = random.Random(SEED) + digits = [digit(s, kind) for _, s, _ in wins] + ups = [e > s for _, s, e in wins] + rets = [(e - s) / s for _, s, e in wins] + n = len(wins) + + chi = chi_square(digits, ups) + shuffled = ups[:] + chi_null = [] + for _ in range(N_PERM): + rng.shuffle(shuffled) + chi_null.append(chi_square(digits, shuffled)) + p_chi = perm_p(chi, chi_null) + + cut = int(n * TRAIN_FRACTION) + tr_d, tr_u, te_d, te_u = digits[:cut], ups[:cut], digits[cut:], ups[cut:] + mapping = fit_map(tr_d, tr_u) + hit = hit_rate(mapping, te_d, te_u) + tr_shuf = tr_u[:] + hit_null = [] + for _ in range(N_PERM): + rng.shuffle(tr_shuf) + hit_null.append(hit_rate(fit_map(tr_d, tr_shuf), te_d, te_u)) + p_oos = perm_p(hit, hit_null) + + long_gross = [r for d, r in zip(te_d, rets[cut:], strict=True) if mapping[d]] + long_net = [(1 + r) * (1 - TAKER) * (1 - TAKER) - 1 for r in long_gross] + shows = p_chi < ALPHA and p_oos < ALPHA + q = Decimal("0.000001") + return { + "arm": arm, + "n_windows": n, + "first_ts": wins[0][0], + "last_ts": wins[-1][0], + "up_rate": Decimal(sum(ups)) / n, + "chi_square": Decimal(str(chi)).quantize(q), + "chi_null_median": Decimal(str(statistics.median(chi_null))).quantize(q), + "p_chi": p_chi.quantize(q), + "n_train": cut, + "n_test": n - cut, + "test_up_rate": Decimal(sum(te_u)) / len(te_u), + "oos_hit_rate": Decimal(str(hit)).quantize(q), + "oos_null_median": Decimal(str(statistics.median(hit_null))).quantize(q), + "oos_null_p95": Decimal(str(sorted(hit_null)[int(0.95 * N_PERM)])).quantize(q), + "p_oos": p_oos.quantize(q), + "n_up_calls": len(long_gross), + "mean_gross_up_call": (sum(long_gross) / len(long_gross)).quantize(q) + if long_gross + else None, + "mean_net_up_call": (sum(long_net) / len(long_net)).quantize(q) if long_net else None, + "median_abs_4h_move": Decimal(statistics.median(abs(r) for r in rets)).quantize(q), + "shows_dependence": shows, + "_series": [r.quantize(q) for r in long_net], + } + + +def main() -> None: + parser = argparse.ArgumentParser(description=__doc__.splitlines()[0]) + parser.add_argument("--db", required=True, help="candle cache (opened read-only)") + parser.add_argument("--out", required=True) + parser.add_argument("--ledger", help="trials ledger to append to (omit to skip)") + args = parser.parse_args() + + results = {} + cache: dict[str, list[tuple[int, Decimal, Decimal]]] = {} + for arm, product, kind in ARMS: + if product not in cache: + cache[product] = windows(_hourly(args.db, product)) + results[arm] = run_arm(arm, cache[product], kind) + + usd_d = results["usd_dollars"]["shows_dependence"] + usd_c = results["usd_cents"]["shows_dependence"] + usdt_d = results["usdt_dollars"]["shows_dependence"] + supported = (usd_d and usdt_d) or usd_c + verdict = "supported" if supported else "not supported" + + with Path(args.out).open("w", encoding="utf-8") as fh: + for arm, row in results.items(): + public = {k: v for k, v in row.items() if k != "_series"} + fh.write(json.dumps({"row": "arm", **public}, default=str) + "\n") + print(json.dumps(public, default=str, indent=1)) + if args.ledger: + append_trial( + args.ledger, + trial_id=f"{SESSION}-{arm}", + session=SESSION, + rule="paxg_last_two_digits", + params={ + "arm": arm, + "end_ts": END_TS, + "train_fraction": str(TRAIN_FRACTION), + "n_perm": N_PERM, + "seed": SEED, + "taker_pct": str(TAKER), + "units": "per_trade_pnl is net return per 'up' call as a fraction, not USD", + "verdict": verdict, + }, + provenance="a_priori", + kind="ablation", + decision="diagnostic_only", + per_trade_pnl=row["_series"], + series_missing=not row["_series"], + summary={ + k: v for k, v in public.items() if k not in ("arm",) and v is not None + }, + ) + fh.write(json.dumps({"row": "verdict", "verdict": verdict}) + "\n") + print(f"verdict: {verdict}") + + +if __name__ == "__main__": + main() diff --git a/docs/experiments/README.md b/docs/experiments/README.md index 9d90f7f3..207eca7c 100644 --- a/docs/experiments/README.md +++ b/docs/experiments/README.md @@ -23,6 +23,15 @@ Bulk sweep output is **not** committed — it is derived data, regenerated from Index is **newest first**, by the date each document carries in its filename. +## 2026-11 + +- [`2026-11-09-paxg-last-two-digits.md`](2026-11-09-paxg-last-two-digits.md) — Do the last two + digits of PAXG's price at a 4-hour window's open predict that window's direction? + **Pre-registered** (driver pushed before the run). **No:** in-sample permutation p 0.10 to 0.74, + out-of-sample hit rate 48.9 to 49.2% against shuffled-label nulls, on Coinbase (dollars and + cents) and five years of Binance. The median 4-hour move of 0.2% is a ninth of the 1.8% taker + round trip anyway. Driver `2026-11-09-paxg-last-two-digits.py`, data `.jsonl`. + ## 2026-09 - [`2026-09-27-accumulation-policy.md`](2026-09-27-accumulation-policy.md) — Static DCA vs diff --git a/docs/experiments/trials-ledger.jsonl b/docs/experiments/trials-ledger.jsonl index f4cbb578..a414e53b 100644 --- a/docs/experiments/trials-ledger.jsonl +++ b/docs/experiments/trials-ledger.jsonl @@ -112,3 +112,6 @@ {"decision":"diagnostic_only","kind":"ablation","params":{"allowance_usd":"500","arm":"B","arm_label":"bounded value averaging, buy-only","block_lengths":[20,60],"deposit_usd":"500","fee_mode":"flat","headline":false,"panel_days":506,"run":"secondary","seed":831,"taker_pct":"0.012","units":"per_trade_pnl is the arm's deposit-neutral account P&L per calendar month on the historical path, in USD; not trades","verdict":"not better than static DCA after fees","weights":{"ADA":"0.06","BTC":"0.3","ETH":"0.2","LINK":"0.06","LTC":"0.06","PAXG":"0.2","SOL":"0.06","XLM":"0.06"},"window_end_ts":1790455996,"window_start_ts":1746662400},"per_bar_pnl":[],"per_trade_pnl":["-5.812824","-26.173048","325.821219","126.238846","56.169394","-210.484701","-555.498844","-118.935502","-369.904245","-360.083363","-89.430718","220.134285","-50.841462","-1182.453841","385.412088","1330.236649","909.987632"],"prev_hash":"fa5927ff39c38f8dff59d4b361a8f01319695a73019f0905f84bad9a50f5fadd","provenance":"a_priori","row_hash":"a6ef33bf9707f5acb68a30244c45cefb60c11469b72893062a73926522059875","rule":"accumulation_policy","series_missing":false,"session":"accumulation-policy-2026-09-27","summary":{"d_sortino_p05_b20":"-0.122861","d_sortino_p05_b60":"-0.161852","d_sortino_p95_b20":"0.190866","d_sortino_p95_b60":"0.236486","headline":false,"hist_avg_cash_share":"0.034886","hist_buy_fees":"102.000000","hist_buy_notional":"8500.000000","hist_cagr_money_weighted":"0.032484","hist_d_mdd":"-0.011235","hist_d_sortino":"0.053318","hist_deposited":"8500.000000","hist_irr":"0.004409","hist_max_drawdown":"0.515197","hist_realized_pnl":"0.000000","hist_sell_fees":"0.000000","hist_sell_notional":"0.000000","hist_sharpe":"0.131206","hist_sortino":"0.189558","hist_terminal_value":"8884.381564","hist_turnover":"1.000000","hist_twr_total":"-0.046928","median_d_mdd_b20":"-0.006070","median_d_mdd_b60":"-0.005324","median_d_sortino_b20":"0.018740","median_d_sortino_b60":"0.019451","n_paths":2000,"p_sortino_positive_b20":"0.610500","p_sortino_positive_b60":"0.595000","passes_b20":false,"passes_b60":false},"timestamp":1790475167,"trial_id":"accumulation-policy-2026-09-27-secondary-flat-B"} {"decision":"diagnostic_only","kind":"ablation","params":{"allowance_usd":"500","arm":"C","arm_label":"deposit steered by shortfall","block_lengths":[20,60],"deposit_usd":"500","fee_mode":"flat","headline":false,"panel_days":506,"run":"secondary","seed":831,"taker_pct":"0.012","units":"per_trade_pnl is the arm's deposit-neutral account P&L per calendar month on the historical path, in USD; not trades","verdict":"not better than static DCA after 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