The following article aims to detect if long-term memory exists in the Mexican exchange rate market. This research was conducted between 1992 and 2016, during which time different intervention mechanisms were presented. The interventions were divided as follows: a) crawling bands (01/1992–12/1994), b) free flotation in crisis (01/1995–07/1996), c) mixed operations with purchases and sales of dollars by the Central Bank (08/1996–06/2001), d) free flotation (07/2001–04/2003), e) accumulation of international reserves (05/2003–02/2009, f) mixed auctions (03/2009–02/2016), and g) free flotation with interest rate increases (03/2016–12/2016). To detect the presence of long-term memory in the peso–dollar exchange rates, we proposed a fuzzy Hurst exponent. The results evidenced distinct types of behaviors depending on the grade of intervention. Compared to a free-floating regime, persistence and fuzzy Hurst values decreased when the Central Bank intervened in the exchange market. On the other hand, uncertainty increased when monetary authorities imposed a mechanism for buying and selling dollars without an exchange rate target.
