BTCautoresearch

Autonomous formula discovery for Bitcoin price prediction, inspired by Karpathy's autoresearch pattern.

An AI agent (Claude) autonomously ran 328 experiments in a single session, searching for the best time-based formula to predict Bitcoin's price. Each experiment modifies a single file (fit.py), evaluates via walk-forward out-of-sample RMSE, and keeps or reverts the change — building a monotonically improving commit history.

Results

50.5% improvement over the standard power law baseline, achieved through 328 autonomous experiments (114 kept).

Prediction RMSE vs Forward Horizon (up to 5 years)

The best model (dark blue) maintains a clear advantage across all horizons, from 1 month to 5 years out-of-sample.

Experiment-by-Experiment Progress

The agent discovers key improvements in phases: mean-reversion correction, local linear extrapolation, Huber-robust fitting, ensemble decay, and shifted power law — then fine-tunes hyperparameters.

Bootstrap Statistical Comparison

Split-level bootstrap (10,000 resamples) comparing three models:

Model	mean RMSE	95% CI	vs baseline
Power law (baseline)	0.267	[0.190, 0.355]	—
Simple last-day decay	0.171	[0.131, 0.219]	-36%
Model T (fully tuned)	0.132	[0.105, 0.162]	-51%

Both models significantly beat the power law. The improvement of Model T over the simple model is not statistically significant (CI includes zero), suggesting the core insight — mean-reversion to the power law — captures most of the achievable gain.

Residual Analysis

Out-of-sample residuals show strong autocorrelation (~250 days), positive skew (bubble underestimation), and halving-cycle structure — indicating exploitable signal remains beyond what calendar time can capture.

The Core Finding

The power law can be significantly improved with a simple modification:

# Fit power law on training data
a, b = polyfit(log10(train_days), train_log_prices, 1)

# Last training day's deviation from trend
r0 = train_log_prices[-1] - (a * log10(train_days[-1]) + b)

# Predict: power law + decaying correction
dt = test_days - train_days[-1]
prediction = a * log10(test_days) + b + r0 * exp(-log(2) * dt / 180)

Interpretation: The power law sets the long-term trend. The correction acknowledges where price is right now relative to trend and decays it toward zero over ~6 months (half-life 180 days). This is mean-reversion to the power law.

Project Structure

├── fit.py          # The mutable model file (agent modifies this)
├── prepare.py      # Read-only evaluation harness (walk-forward, multi-horizon)
├── program.md      # Agent instructions (the autoresearch protocol)
├── btc_daily_prices.csv  # Daily BTC price data (2009–2026)
├── results.tsv     # Full experiment log (328 experiments)
└── pyproject.toml  # Dependencies: numpy, scipy, matplotlib

How to Use

Prerequisites

• Python 3.10+
• uv package manager
• An AI coding agent (Claude Code, Cursor, Codex, etc.)

Setup

git clone https://github.com/CBaquero/BTCautoresearch.git
cd BTCautoresearch
uv sync

Run the Current Best Model

uv run fit.py

Start a New Experiment Loop

Point your AI agent at the repo and say:

Read program.md and start a new experiment loop. Tag: <your-tag>

The agent will:

1. Create a branch autoresearch/<tag>
2. Read prepare.py (read-only rules) and fit.py (what to modify)
3. Run the baseline: uv run fit.py
4. Loop: edit fit.py → commit → run → keep if improved, revert if not
5. Log results to results.tsv

Tips:

• Use --dangerously-skip-permissions for unattended runs
• Sonnet-class models work well for this task (good at code editing, fast)
• Each experiment takes ~1-2 seconds (curve fitting, not ML training)
• Expect ~20-30 experiments/hour, limited by agent thinking time

Evaluation Protocol

prepare.py implements strict walk-forward validation:

• 9 splits: 2016–2024 (expanding training window)
• 7 horizons: 1, 3, 6, 12, 18, 24, 36 months forward
• Metric: mean RMSE of log10(price) across all 63 evaluations
• No future information: model receives only training data at each split

License

MIT