A Framework for Predictive Directional Trading Based on Volatility and Causal Inference

Paper: arXiv 2507.09347

Authors: Ivan Letteri

Abstract

Purpose: This study introduces a novel framework for identifying and exploiting predictive lead-lag relationships in financial markets. We propose an integrated approach that combines advanced statistical methodologies with machine learning models to enhance the identification and exploitation of predictive relationships between equities. Methods: We employed a Gaussian Mixture Model (GMM) to cluster nine prominent stocks based on their mid-range historical volatility profiles over a three-year period. From the resulting clusters, we constructed a multi-stage causal inference pipeline, incorporating the Granger Causality Test (GCT), a customised Peter-Clark Momentary Conditional Independence (PCMCI) test, and Effective Transfer Entropy (ETE) to identify robust, predictive linkages. Subsequently, Dynamic Time Warping (DTW) and a K-Nearest Neighbours (KNN) classifier were utilised to determine the optimal time lag for trade execution. The resulting strategy was rigorously backtested. Results: The proposed volatility-based trading strategy, tested from 8 June 2023 to 12 August 2023, demonstrated substantial efficacy. The portfolio yielded a total return of 15.38%, significantly outperforming the 10.39% return of a comparative Buy-and-Hold strategy. Key performance metrics, including a Sharpe Ratio up to 2.17 and a win rate up to 100% for certain pairs, confirmed the strategy’s viability. Conclusion: This research contributes a systematic and robust methodology for identifying profitable trading opportunities derived from volatility-based causal relationships. The findings have significant implications for both academic research in financial modelling and the practical application of algorithmic trading, offering a structured approach to developing resilient, data-driven strategies.

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 6.0/10 (capped from 7.0: transaction costs only partially modelled; see penalty flags)
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper employs a sophisticated mathematical pipeline combining GMM clustering, multiple causal inference tests (Granger, PCMCI, Transfer Entropy), and DTW for lag optimization, indicating high mathematical density. While the backtest results show strong performance metrics and a defined testing period, the absence of publicly available code or datasets and reliance on a specific, short out-of-sample window slightly limits the empirical rigor compared to a fully reproducible study.

Research Flowchart

  flowchart TD
  A["Research Goal"] -->|Identify lead-lag relationships| B["Data Preprocessing"]
  B --> C["Variance Reduction<br>GMM Clustering"]
  C --> D["Reliability Assessment<br>Multi-stage Causal Pipeline"]
  D -->|GCT, PCMCI, ETE| E["Trade Signal Generation<br>DTW + KNN"]
  E --> F["Strategy Execution"]
  F --> G["Performance Evaluation"]
  
  style A fill:#e1f5fe
  style G fill:#e8f5e8
  style D fill:#fff3e0

Cited References (34)

1. VolTS: A Volatility-based Trading System to forecast Stock Markets Trend using Statistics and Machine Learning (2023) — link
2. VolTS Augmented: An Improvement of a Volatility-based Trading System to Forecast Stock Markets Trends (2024) — link
3. DNN-ForwardTesting: A New Trading Strategy Validation using Statistical Timeseries Analysis and Deep Neural Networks (2022) — link
4. Forecasting intraday volatility in the US equity market. Multiplicative component GARCH (2012) — link
5. Pairs trading: Performance of a relative-value arbitrage rule (2006)
6. How Crashes Develop: Intradaily Volatility and Crash Evolution (2019) — link
7. Volatility and Correlation Forecasting (2006) — link
8. K-Means++: The Advantages of Careful Seeding (2007)

0 of 34 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.