Frequency Structure of AMM Liquidity Pools: A Multiresolution Analysis of Regime Transitions
This study examines the temporal structure of liquidity pools in constant-product automated market makers. Using a sample of eighteen pools observed at a five-minute frequency over two years, it aims to identify the temporal scales at which interactions within the system occur and how these interactions reorganize in response to changes in the volatility regime. Methodologically, the study proposes a strictly causal Haar multiresolution analysis in which each variable is estimated using only the information available at the time of measurement. Within this decomposition, three dimensions are examined: the scale composition of the return-to-risk relationship, the frequency-band coupling between pool activity and price volatility, and the detection of regime transitions using a fluctuation-to-trend indicator. The results reveal a clear structural segmentation: pool variability is concentrated at fast scales, whereas the relationships among its series, signal persistence, and information on subsequent performance reside at slow scales. Aggregate measures do not distinguish this separation because they combine both components before they can be compared.