Spatio-Temporal Momentum: Jointly Learning Time-Series and Cross-Sectional Strategies

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Spatio-Temporal Momentum: Jointly Learning Time-Series and Cross-Sectional Strategies

Wee Ling Tan
Stephen Roberts
Stefan Zohren
Published on 2/20/2023
Equities
Futures
United States (US)
Momentum
Momentum in stocks
Machine learning
Deep learning
Backtesting
Factor investing

This paper introduces Spatio-Temporal Momentum (STMOM), a novel framework that jointly learns time-series and cross-sectional momentum strategies using multitask learning. Unlike traditional approaches that treat these strategies separately, STMOM models the trading signals for all assets simultaneously by feeding a spatio-temporal tensor of momentum features (volatility-normalized returns and MACD) into a neural network. The network is trained end-to-end to maximize the portfolio Sharpe ratio, directly outputting positions for each asset without requiring manual ranking or decile allocation. The authors evaluate several architectures—single-layer perceptron (SLP), multilayer perceptron (MLP), convolutional neural network (CNN), and long short-term memory (LSTM)—on portfolios of 46 US equities and 12 equity index futures. Backtesting from 1990–2022 (equities) and 2003–2020 (futures) shows that the simplest SLP with L1 regularization consistently outperforms more complex models and classical benchmarks (TSMOM, MACD, CSMOM, and deep momentum networks). After portfolio-level volatility scaling, the SLP achieves Sharpe ratios of 2.61 for equities and 1.73 for futures, significantly exceeding the next best method. The paper also demonstrates that STMOM retains its edge under high transaction costs (5–10 basis points) when combined with turnover regularization. The authors attribute the success of the simple SLP to the low signal-to-noise ratio of financial data and limited training samples, which cause complex models to overfit. Overall, STMOM provides a unified, data-driven approach to momentum investing that leverages cross-asset information and directly optimizes risk-adjusted returns.

Highlights

  • 1Unifies time-series and cross-sectional momentum into a single spatio-temporal framework using multitask learning.
  • 2Demonstrates that a simple single-layer perceptron (SLP) with L1 regularization outperforms more complex architectures like LSTM and CNN.
  • 3Achieves superior risk-adjusted returns compared to classical momentum strategies and deep momentum networks (DMN) on US equities and equity index futures.
  • 4Retains performance under high transaction costs (5-10 bps) when combined with turnover regularization.
  • 5Directly optimizes the Sharpe ratio in a multi-asset setting, bypassing manual ranking and decile-based allocation.

Methods

  • M
    Multitask learning with neural networks (SLP, MLP, CNN, LSTM) to jointly predict trading signals for all assets.
  • M
    Sharpe ratio optimization as the loss function, with L1 shrinkage and turnover regularization.
  • M
    Spatio-temporal input tensor combining volatility-normalized returns and MACD features across assets and time.
  • M
    Expanding window backtesting with rolling retraining every 5 years.

Results

  • R
    SLP spatio-temporal momentum achieves Sharpe ratios of 2.61 (US equities) and 1.73 (futures) after volatility scaling, outperforming DMN (2.92 and 0.41) and benchmarks.
  • R
    Complex models (MLP, LSTM, CNN) underperform the simple SLP, likely due to overfitting and limited data.
  • R
    Cross-sectional momentum (CSMOM) yields negative returns in both datasets.
  • R
    Turnover regularization reduces transaction costs impact, maintaining profitability up to 10 bps costs.
  • R
    Portfolio-level volatility scaling significantly improves performance of STMOM strategies (e.g., SLP Sharpe increases by 134% for equities).
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