Empirical Analysis of Lookback Window Optimization in Pairs Trading Using Fast Fourier Transform

This study introduces a novel approach for optimizing the lookback window in pairs trading using Fast Fourier Transform (FFT). We validate this approach by applying it to copper futures (CU) on the Shanghai Futures Exchange and silicon iron futures (SF) on the Zhengzhou Commodity Exchange. The prices of CU and SF exhibit non-stationary yet cointegrated dynamics over the study period, making the time series suitable for testing. Through frequency domain analysis, FFT identifies the dominant periodic component within the price ratio of two assets, which serves as a reference point for window selection. Backtesting on various lookback windows demonstrates that those centered around the FFT-extracted cycle yield superior performance, effectively aligning trading windows with the natural periodicity of asset ratios. Our experiment confirms that FFT-based period extraction provides a suitable basis for selecting lookback windows, enhancing signal accuracy in cointegration-based pairs trading strategies. This methodology contributes a new perspective to pairs trading, leveraging frequency domain insights to advance window selection in cointegration-based frameworks.