We present an application of the switching linear dynamical model (SLDM) to model the nominal Mexican peso-USD exchange rate time series from January 01, 1970 to January 09, 2019. Two main features exhibited by the time series are observed: dynamical behavior with upward and downward movements after moving to the floating exchange rate regime, and most recently a persistent increasing trend. The SLDM is a flexible method for learning about dynamic models for time series with complex and uncertain behavior patterns, such as those exhibited by the exchange rate. The SLDM allows us to account for four novel results not obtained before: (1) we are able to identify four regimes; (2) we cluster the observations into regimes; (3) we provide the estimated probability of a change point at each time instead of estimating a regime constant persistence; and (4) we find that the change points match with some internal and external events associated with crisis periods.