How to Identify Varying Lead-Lag Effects in Time Series Data: Implementation, Validation, and Application of the Generalized Causality Algorithm

This paper develops the generalized causality algorithm and applies it to a multitude of data from the fields of economics and finance. Specifically, our parameter-free algorithm efficiently determines the optimal non-linear mapping and identifies varying lead-lag effects between two given time series. This procedure allows an elastic adjustment of the time axis to find similar but phase-shifted sequences-structural breaks in their relationship are also captured. A large-scale simulation study validates the outperformance in the vast majority of parameter constellations in terms of efficiency, robustness, and feasibility. Finally, the presented methodology is applied to real data from the areas of macroeconomics, finance, and metal. Highest similarity show the pairs of gross domestic product and consumer price index (macroeconomics), S&P 500 index and Deutscher Aktienindex (finance), as well as gold and silver (metal). In addition, the algorithm takes full use of its flexibility and identifies both various structural breaks and regime patterns over time, which are (partly) well documented in the literature.