Phantom: Distributional Forecasting for Cross-Sectional Cryptocurrency Return Prediction

A Transformer-based model that predicts full Student-t distributions of cross-sectional relative returns across 362 cryptocurrencies at horizons of 1-30 days, using only standard OHLCV price and volume features.

Paper: paper/main.tex | Release: v1.0 (checkpoints + data)

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Key Results (fully out-of-sample, Jan 2025 - Mar 2026)

Metric	Value
Rank IC (10d)	0.124 (Newey-West t = 8.93)
Long-Short Sharpe (net 30 bps)	11.84
Win Rate	74.7% daily
Decile Monotonicity	1.000 (perfect)
Breakeven Cost	336 bps
IC Positive Months	15/15

Main Results

(a) Rank IC increases with horizon (0.08 at 1d to 0.17 at 30d). (b) Long-short cumulative returns survive 30 bps transaction costs. (c) Perfect decile monotonicity. (d) Phantom dominates all baselines.

Robustness

IC positive in all 15 months. Rolling 60-day Sharpe always > 0 (min = 2.82). Turnover stable at 38%.

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Architecture

• Encoder: 8-layer pre-norm Transformer on 24 patches of 120-day, 6-channel OHLCV input (512d, 8 heads)
• Decoder: 2-layer cross-attention decoding all 30 horizons simultaneously
• Head: Student-t output (mu, sigma, nu) per horizon - 3 parameters, no mixture
• Anti-collapse: Condition dropout (p=0.15) + encoder variance penalty
• Parameters: 31.7M

Approach

The model predicts relative returns (asset return minus cross-sectional mean), isolating idiosyncratic signal from shared market factors. This is the key insight that unlocks cross-sectional predictability:

• Absolute returns from OHLCV are unpredictable at any horizon (consistent with weak-form EMH)
• Relative returns contain ranking signal concentrated in crypto (IC = 0.124)

Two-Stage Training

1. Stage 1: Pretrain on 413 assets (crypto + equities + forex + commodities) with 6-channel OHLCV features
2. Stage 2: Fine-tune on 362 crypto assets only - the signal concentrates in crypto

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Ablation: What Works and What Doesn't

Eight model versions systematically test the design space:

Version	Change	IC (10d)	Sharpe	Finding
v1-v2	Synthetic SDE pretrain	-	-	Oracle CRPS on synthetic, zero transfer to real
v3	Real multi-asset pretrain	0.00	-	Good calibration, no directional signal
v4	Multi-horizon absolute returns	0.00	-	Memorizes training, doesn't generalize
v5	Relative returns	0.09	4.6	Signal unlocked
v6	+ Funding rate, taker buy	0.14	5.5	Features don't help; crypto-only helps
v7	4h bars	0.10	2.6	Worse: 99.7% sample overlap, signal is daily
v8	362 crypto assets	0.12	13.0	Sharpe doubles via diversification

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Quick Start

pip install -r requirements.txt

# Download checkpoint and data from release
# https://github.com/ADnocap/phantom/releases/tag/v1.0

# Evaluate
python scripts/eval/eval_v5.py \
    --checkpoint checkpoints_v8/best.pt \
    --test_data data/processed_v8/test.npz

# Full publication analysis (transaction costs, baselines, robustness)
python scripts/eval/publication_analysis.py \
    --checkpoint checkpoints_v8/best.pt \
    --test_data data/processed_v8/test.npz

# Train from scratch (requires data fetching first)
python scripts/data/fetch_crypto_v8.py --workers 6
python scripts/data/build_dataset_v8.py
python scripts/train/train_pretrain.py \
    --data_mode v5_real_assets \
    --real_data_dir data/processed_v8/ \
    --init_from checkpoints_v5/best.pt \
    --head_type student_t \
    --n_input_channels 6 \
    --context_len 120 --max_horizon 30 \
    --d_model 512 --n_layers 8 --n_heads 8 --d_ff 2048 \
    --batch_size 512 --epochs 50 --lr 3e-4

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Project Structure

phantom/
├── src/
│   ├── model.py              # PhantomModel (encoder + cross-attn decoder + Student-t head)
│   ├── losses.py             # NLL, CRPS, energy distance, combined losses
│   ├── features.py           # 6-channel OHLCV feature computation
│   ├── real_data.py          # Dataset classes for processed .npz files
│   ├── data.py               # Online synthetic dataset (v1/v2 only)
│   ├── sde.py                # SDE simulators (v1/v2 only)
│   └── btc_data.py           # BTC OHLCV fetching
├── scripts/
│   ├── train/
│   │   ├── train_pretrain.py # Main training script (v3-v8)
│   │   ├── train_v6.py       # v6 crypto fine-tuning with new features
│   │   ├── train_v7.py       # v7 4h-bar training
│   │   └── train_finetune.py # BTC fine-tuning (v1/v2)
│   ├── eval/
│   │   ├── eval_v5.py        # Cross-sectional evaluation (IC, Sharpe, coverage)
│   │   ├── publication_analysis.py  # Full publication analysis
│   │   └── ...
│   ├── data/
│   │   ├── fetch_crypto_v8.py    # Fetch all Binance USDT pairs
│   │   ├── build_dataset_v8.py   # Build crypto-only dataset
│   │   └── ...
│   └── slurm/                # HPC job scripts (LaRuche A100)
├── paper/
│   └── main.tex              # Paper (ACM sigconf format)
├── notebooks/
│   └── phantom_v5_analysis.ipynb  # Interactive analysis
├── plots/                    # All figures
├── logs/                     # Training CSV logs
├── experiments.md            # Full experiment log (v1-v8)
└── CLAUDE.md                 # Project instructions

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References

• Liu, Tsyvinski, Wu (2022). Common Risk Factors in Cryptocurrency. Journal of Finance, 77(2):1133-1177.
• Fieberg et al. (2024). A Trend Factor for the Cross Section of Cryptocurrency Returns. JFQA.
• Hackmann (2026). JointFM: A Joint Foundation Model for Distributional Prediction. arXiv:2603.20266.
• Nie et al. (2023). A Time Series is Worth 64 Words. ICLR 2023.
• Gneiting & Raftery (2007). Strictly Proper Scoring Rules, Prediction, and Estimation. JASA, 102(477):359-378.