Time-varying leads and lags across frequencies using a continuous wavelet transform approach

- Lead-lag structures in economic data are relevant to many economic agents.
- Wavelet phase difference can capture changing leads and lags across frequencies.
- Different interpretations of phase difference coexist in the literature.
- We deliberate on which interpretation can be considered plausible.
- Our deliberation reaches a correct lead-lag interpretation of phase difference.

A precise understanding of lead-lag structures in economic data is important for many economic agents such as policymakers, traders in financial markets, and producers in goods markets. To identify time-varying lead-lag relationships across various frequencies in economic time series, recent studies have used phase difference on the basis of a continuous wavelet transform. However, the extant literature includes several conflicting interpretations of phase difference. In this study, we extensively discuss wavelet phase difference, determine its most plausible interpretation, and thus attempt to address gaps in the existing literature. Consequently, this study suggests that some lead-lag results of previous works have been driven by incorrect interpretations of wavelet phase difference.