Using Multi-Dimensional Dynamic Time Warping to Identify Time-Varying Lead-Lag Relationships

This paper develops a multi-dimensional Dynamic Time Warping (DTW) algorithm to identify varying lead-lag relationships between two different time series. Specifically, this manuscript contributes to the literature by improving upon the use towards lead-lag estimation. Our two-step procedure computes the multi-dimensional DTW alignment with the aid of shapeDTW and then utilises the output to extract the estimated time-varying lead-lag relationship between the original time series. Next, our extensive simulation study analyses the performance of the algorithm compared to the state-of-the-art methods Thermal Optimal Path (TOP), Symmetric Thermal Optimal Path (TOPS), Rolling Cross-Correlation (RCC), Dynamic Time Warping (DTW), and Derivative Dynamic Time Warping (DDTW). We observe a strong outperformance of the algorithm regarding efficiency, robustness, and feasibility.