Time-varying coefficient DAR model and stability measures for stablecoin prices: An application to Tether

Abstract

This paper examines the dynamics of Tether, the stablecoin with the largest market capitalization. We show that the distributional and dynamic properties of Tether/USD rates have been evolving between 2017 - 2021. We use local analysis methods to detect local trends and time-varying volatility and persistence. To accommodate these dynamic patterns, we introduce the time-varying parameter Double Autoregressive tvDAR(1) process under the assumption of local stationarity of Tether/USD rates. We also propose a set of simple plug-in measures of stability based on the Lyapunov exponent for assessing and comparing the stability of Tether and other stablecoins. We show the consistency of stability measure estimators and study their distributional properties. The tvDAR model is estimated on Tether prices and compared with other stablecoins. We find that it provides good fit to data with time-varying persistence and volatility and produces reliable out-of-sample forecasts at short horizons. In the application, the proposed stability measures provide reliable indicators of local explosive patterns for stablecoin monitoring.