This study analyzes the presence of long memory in the USD and EUR exchange rate parities in Turkey using ARFIMA (Autoregressive Fractionally Integrated Moving Average) models. The analysis is conducted on weekly data covering the period 2010–2024. Empirical findings indicate that both the USD and EUR exchange rate series exhibit long memory, although the strength of this memory is relatively low. This suggests that the effects of past shocks in the exchange rate series weaken and dissipate over time. Moreover, the study finds that the Turkish foreign exchange market does not exhibit a fully stable structure, thereby offering short-term arbitrage opportunities for investors. The presence of long memory in weekly exchange rate returns implies that the market does not fully conform to the Efficient Market Hypothesis (EMH). These results are particularly relevant for long-term asset investors and provide insights into the dynamics of the foreign exchange market for policymakers and market participants. Overall, the study highlights both the long memory phenomenon in exchange rates and the structural characteristics of Turkey’s FX markets, offering guidance for market regulation and risk management strategies.