  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 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.
