Novel Aligned Correlation Method to Estimate Lead–Lag Relationship Between Time Series

ABSTRACT Lead–lag relationship where a lagging time series partially replicates the movement of a leading time series, is frequently observed in financial time series data. Empirical estimation of this lead–lag relationship is challenging due to the excessive noise present in time series data. The present research work proposes a new technique that helps better identify the lead–lag relationship empirically. Further, it gives a measure (aligned correlation) that estimates the distance between two time series after adjusting for any lead–lag relationship between the two series. The proposed technique is compared with existing state‐of‐the‐art techniques, dynamic time warping (DTW) and thermal optimal path (TOP). Tests are performed on synthetic time series (STS) with known lead–lag relationship and comparisons are done on the basis of statistical significance and forecast accuracy. The proposed technique gives the best results in terms of both these criteria. It finds lead–lag paths between the time series that are all statistically significant, and its forecasts of the lagging time series made using the leading time series are closest to the actual values. Further experiments conducted on a financial time series dataset and an ECG dataset reveal the effectiveness of the proposed methodology.