A Learnable Wavelet Transformer for Long-Short Equity Trading and Risk-Adjusted Return Optimization

TL;DR

The paper tackles the challenge of learning profitable intraday trading policies under noisy, non-stationary financial time series with cross-asset dependencies. It introduces WaveLSFormer, a learnable wavelet front-end coupled with a Transformer, and a low-guided high-frequency injection mechanism to fuse multi-scale information while maintaining training stability. Training optimizes a trading-oriented objective that blends soft-label supervision, ROI/Sharpe regularization, and a neural wavelet loss to enforce stable frequency separation, all under a fixed risk budget. Extensive experiments across five years of hourly U.S. equity data and six industry groups show WaveLSFormer consistently outperforms MLP, LSTM, and Transformer baselines, achieving an average ROI of $0.607 \pm 0.045$ and Sharpe of $2.157 \pm 0.166$, with notable improvements in profitability and risk-adjusted returns. The work demonstrates a practical, end-to-end approach to intelligent trading that leverages learnable time-frequency decomposition and frequency-aware fusion for robust, scalable decision making.

Abstract

Learning profitable intraday trading policies from financial time series is challenging due to heavy noise, non-stationarity, and strong cross-sectional dependence among related assets. We propose \emph{WaveLSFormer}, a learnable wavelet-based long-short Transformer that jointly performs multi-scale decomposition and return-oriented decision learning. Specifically, a learnable wavelet front-end generates low-/high-frequency components via an end-to-end trained filter bank, guided by spectral regularizers that encourage stable and well-separated frequency bands. To fuse multi-scale information, we introduce a low-guided high-frequency injection (LGHI) module that refines low-frequency representations with high-frequency cues while controlling training stability. The model outputs a portfolio of long/short positions that is rescaled to satisfy a fixed risk budget, and is optimized directly with a trading objective and risk-aware regularization. Extensive experiments on five years of hourly data across six industry groups, evaluated over ten random seeds, demonstrate that WaveLSFormer consistently outperforms MLP, LSTM and Transformer backbones, with and without fixed discrete wavelet front-ends. On average in all industries, WaveLSFormer achieves a cumulative overall strategy return of $0.607 \pm 0.045$ and a Sharpe ratio of $2.157 \pm 0.166$, substantially improving both profitability and risk-adjusted returns over the strongest baselines.

Figures (11)

• Figure 1: Stock codes selected under DWT.
• Figure 2: Stock selected after Granger causality filter in the renewable energy industry.
• Figure 3: Loss curve and gradient of tanh and soft-label loss functions
• Figure 4: Strategy return curve of renewable energy
• Figure 5: Strategy return curve of retail consumer goods