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E-TRENDS: Enhanced LSTM Trend Forecasting for Equities

Harris Buchanan, Eric Benhamou

Abstract

Trend-following strategies underpin many systematic trading approaches yet struggle under nonstationary and nonlinear market regimes. We propose an LSTM-based framework to forecast next-day trend differences ($Δ_t$) for the top 30 S\&P 500 equities, validated across market cycles (2005--2025). Key contributions include: (i) formal proof of bias-variance reduction via differencing, (ii) exhaustive empirical benchmarks against OLS, Ridge, and Lasso, (iii) portfolio simulations confirming economic gains in terms of overall PNL compared to other models like OLS, Ridge, Lasso or LightGBM Regressor

E-TRENDS: Enhanced LSTM Trend Forecasting for Equities

Abstract

Trend-following strategies underpin many systematic trading approaches yet struggle under nonstationary and nonlinear market regimes. We propose an LSTM-based framework to forecast next-day trend differences () for the top 30 S\&P 500 equities, validated across market cycles (2005--2025). Key contributions include: (i) formal proof of bias-variance reduction via differencing, (ii) exhaustive empirical benchmarks against OLS, Ridge, and Lasso, (iii) portfolio simulations confirming economic gains in terms of overall PNL compared to other models like OLS, Ridge, Lasso or LightGBM Regressor
Paper Structure (53 sections, 1 theorem, 12 equations, 2 figures, 5 tables)

This paper contains 53 sections, 1 theorem, 12 equations, 2 figures, 5 tables.

Table of Contents

  1. Introduction
  2. Motivation and research question
  3. Contribution to the literature
  4. Overview of main findings
  5. Structure of the Paper
  6. Literature Review
  7. Traditional trend‐following strategies
  8. Statistical signal construction (t‐statistics, rolling measures)
  9. Machine learning in asset‐pricing and trading
  10. Gaps and how this work addresses them
  11. Data Description
  12. Asset universe and sample period
  13. Data sources and preprocessing
  14. Summary statistics
  15. Theoretical Justification: Differencing and Variance Reduction
  16. ...and 38 more sections

Key Result

Theorem 1

Let $y_t = m_t + \varepsilon_t$, where $m_t$ is a smooth deterministic trend and $\varepsilon_t$ is a stationary noise process with zero mean and finite variance. Define $\Delta_t := y_t - y_{t-1}$, and let $f_y$ and $f_\Delta$ be Lipschitz-continuous estimators trained to predict $m_t$ and $\delta_ That is, differencing reduces estimator variance while inflating bias at most linearly in the local

Figures (2)

  • Figure 1: Predicted vs. Actual Trend Change Signal for NVDA (50-day lookback). The blue line is the actual $\Delta_t$ series shifted by one day; the orange line is the LSTM’s predicted signal.
  • Figure 2: Cumulative P&L of baseline vs. LSTM strategy for NVDA (2005–2025).

Theorems & Definitions (2)

  • Theorem 1: Bias–Variance Tradeoff under Differenced Forecasting
  • proof