HMM Uncertainty Signals in Optimal Trade Execution

This study asks whether HMM-derived confidence scores can predict when regime-aware execution outperforms TWAP, and at what temporal resolution that prediction holds.

Prior work (see companion paper below) showed that RL agents cannot exploit regime signals even when the true label is in the state space. This study asks a simpler question: can hand-crafted HMM uncertainty signals at least predict when the regime-aware rule works? The answer turns out to depend critically on the evaluation horizon.

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Research Questions

1. Do HMM confidence scores predict regime-aware execution quality on real assets?
2. At what temporal resolution does predictive power emerge?
3. Which uncertainty signal, composite confidence, raw entropy, or stay probability, is most informative, and does this vary across asset classes?

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Key Findings

Asset	Signal	Horizon	Spearman ρ	p-value
IWM	Raw entropy	10-day	−0.411	< 0.001 ✓
BTC-USD	Raw entropy	10-day	−0.190	< 0.001
BTC-USD	Stay probability	10-day	−0.204	< 0.001
GLD	Raw entropy	10-day	−0.167	0.013
ETH-USD	Stay probability	10-day	−0.110	0.044
TLT	Stay probability	10-day	−0.318	< 0.001

Negative ρ = higher uncertainty predicts worse regime-aware execution (correct direction).
IWM entropy is the primary finding: survives Bonferroni correction and 100% of bootstrap resamples are negative.

Core result: Daily signals are largely uninformative. Predictive power emerges at 3-day aggregation and stabilises by 10 days. Raw entropy outperforms composite confidence for equity indices; stay probability is more informative for long-duration cryptocurrency assets. QQQ shows no consistent signal and serves as a case study in data-period sensitivity for sector-concentrated indices.

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Setup

git clone https://github.com/satishgarg/hmm-uncertainty-signals
cd hmm-uncertainty-signals
pip install -r requirements.txt

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Reproducing Results

python run_analysis.py          # full pipeline: downloads data, fits HMMs, runs all tests

All data is downloaded automatically via yfinance (internet required).
Analysis uses a rolling one-year window ending at the time of the run; results will reflect current market conditions rather than a fixed historical snapshot.
Outputs are written to results/ and figures/ (created automatically on first run). Expected runtime: ~5–10 minutes on a standard CPU.

To reproduce individual tables:

python rolling_window_test.py   # Table 6: signal emergence across horizons
python alt_execution_test.py    # Table 5: execution model sensitivity
python seed_robustness_test.py  # Table 4: bootstrap stability (1000 resamples)

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Structure

├── alt_execution_test.py     # Table 5: execution model sensitivity (±10% noise)
├── analysis_core.py          # Spearman tests, filter comparison, threshold sweep
├── data_collector.py         # Downloads OHLCV, computes signals and execution costs
├── plotting.py               # Publication figures
├── regime.py                 # 4-state HMM fitting, smoothing, walk-forward labelling
├── report.py                 # Summary printout and CSV export
├── requirements.txt
├── rolling_window_test.py    # Table 6: signal emergence across W ∈ {1,3,5,10,21}
├── run_analysis.py           # Entry point: runs full pipeline end-to-end
├── seed_robustness_test.py   # Table 4: bootstrap stability for primary findings

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What Each Script Does

regime.py: Core HMM module. Fits a 4-state Gaussian HMM (crash, bearish, transitional, bullish) with BIC-based covariance selection (diagonal vs full), state identification by return + trend score, minimum-duration smoothing to suppress single-day regime switches, and walk-forward out-of-sample labelling where sample size permits.

data_collector.py: Downloads daily OHLCV for all eight assets, fits the HMM, and computes per-day metrics: composite confidence, raw posterior entropy, stay probability, regime duration, and execution cost difference (regime-aware minus TWAP). Outputs data/raw_backtest_data.json (generated on each run).

analysis_core.py: Four analyses: (1) confidence distribution characterisation, (2) Spearman correlation between each signal and execution cost difference, (3) alternative filter comparison across entropy / regime duration / stay probability, (4) binary threshold sweep over θ ∈ [0.30, 0.90].

rolling_window_test.py: Replicates the temporal aggregation analysis, testing all three signals at W ∈ {1, 3, 5, 10, 21} days and saving figures/signal_emergence.png.

alt_execution_test.py: Adds ±10% Gaussian noise to cost differences and re-runs Spearman tests for key asset–signal pairs to test sensitivity to fill model misspecification.

seed_robustness_test.py: Bootstrap stability via 1000 resamples for IWM entropy and BTC-USD stay probability at W = 10.

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Assets and Data

Eight assets via yfinance, rolling one-year window of daily OHLCV:

Asset	Class	n (days)
SPY, QQQ, IWM	Equity ETF	~230
BTC-USD, ETH-USD	Cryptocurrency	345
GLD	Commodity ETF	~230
TLT	Bond ETF	~230
AAPL	Large-cap equity	~230

Execution costs are simulated from OHLCV prices. No live order or tick data is used.

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Notes on Limitations

All results use in-sample HMM fitting. Walk-forward out-of-sample validation requires ≥ 20 windows (minimum n ≈ 672 days); no asset in this sample meets that threshold. Reported effect sizes should be treated as upper bounds on out-of-sample predictive power. Because the analysis uses a rolling data window, specific point estimates will shift as the trailing year advances.

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Companion Paper

This paper extends:

Garg, S. (2025). Regime Awareness in RL for Optimal Trade Execution: A Simulation Study. SSRN preprint 6559598.
https://papers.ssrn.com/abstract=6559598

That study showed flat PPO cannot exploit regime signals even with the true label in the state space. This study asks the prior question: are the signals empirically predictive at all, and at what timescale?

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Built On

• Amrouni et al. (2022): CTMSTOU simulation environment (JP Morgan AI Research)
• hmmlearn: HMM fitting
• yfinance: Market data