Comment: 53 pages, 10 figuresThis 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 from 2017 to 2021. We use local analysis methods to detect and describe the local patterns, such as short-lived trends, time-varying volatility and persistence. To accommodate these patterns, we consider a time varying parameter Double Autoregressive tvDAR(1) model under the assumption of local stationarity of Tether/USD rates. We estimate the tvDAR model non-parametrically and test hypotheses on the functional parameters. In the application to Tether, the model provides a good fit and reliable out-of-sample forecasts at short horizons, while being robust to time-varying persistence and volatility. In addition, the model yields a simple plug-in measure of stability for Tether and other stablecoins for assessing and comparing their stability.