The paper looks at currency exchange rates through the lens of a mathematical procedure known as a wavelet analysis. The authors use two statistical parameters, the Hurst coefficient and the gamma coefficient, to determine the compliance of their method with what is called Generalized Pareto Distribution (GPD). The Hurst coefficient is a measure of the randomness of a process and shows how it changes. The gamma coefficient provides information on the dependence/independence of variables generating the process. In the case of currency exchange rates, the main variables are key economic factors and decisions made by monetary policy makers. The analysis applies to a period in the past when Poland’s exchange rate system became more flexible. Depending on changes made in the exchange rate system, the authors identified periods of a uniform exchange rate policy and the stage of a free market rate. They zeroed in on daily changes in the dollar/zloty and euro/zloty rates, in addition to other factors.