Symbolic Fourier Approximation for Pruned Time-Series Similarity Search

Summary

This article develops Symbolic Fourier Approximation (SFA), a way to encode normalized price windows as short symbolic words for similarity search. It replaces SAX’s piecewise-average representation with selected low-frequency Fourier coefficients, then learns quantization boundaries separately for each coefficient position from training windows. Because coefficient spreads differ, the learned bins aim to use the available alphabet more evenly. The method also derives a lower bound that allows historical analogs to be pruned before exact distance calculations.

The article describes validation checks and a comparison harness that evaluates SFA and SAX on identical windows, including bound behavior, pruning, symbol changes under noise, and neighbor recall. It reports that SFA’s advantage is greatest when the bit budget favors a deeper alphabet over more positions, and diminishes with many shallow positions. The evidence is limited: the main experiment used EURUSD H1, with other symbol and timeframe checks at one configuration; walk-forward refitting was not tested, and the 48-bar window is shorter than common research examples. The transform also uses more arithmetic than SAX.

Key ideas

• SFA encodes windows using truncated Fourier coefficients instead of SAX’s piecewise aggregate means.
• Multiple Coefficient Binning learns quantization boundaries separately for each coefficient position.
• A lower bound on series distance supports pruning during historical analog search.
• The reported comparison favors SFA most when the encoding uses a deeper alphabet and fewer positions.
• The experiments leave longer windows and walk-forward refitting untested, and SFA costs more arithmetic than SAX.

Tags

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.