Correlation analysis in time series of fruit prices produced in the Sao Francisco Valley

Agribusiness is a significant economic activity in Brazil, representing 26.6% of the GDP in 2020. Fruit farming is a prominent sector, contributing to both the domestic and international markets and generating millions of direct jobs. The total production of fresh fruits in 2020 exceeded 44 million tons, positioning Brazil as the third-largest fruit producer in the world. Among the key fruits, mango and grapes stand out, ranking first and third in exports. This study analyzes the prices of two varieties of mango (Palmer and Tommy Atkins) and two of grapes (Italia and Benitaka) produced in the Sao Francisco Valley, a region of relevance for these productions and exports. The weekly average price data were obtained from the Center for Advanced Studies in Applied Economics (CEPEA/USP). Using the obtained price series, we calculated logarithmic returns and volatility. We applied the Detrended Fluctuation Analysis (DFA) and Detrended Cross-Correlation Analysis (DCCA) methods, which are useful for identifying the presence of autocorrelation and correlations between two time series simultaneously. The cross-correlation coefficient (rho DCCA) was used to infer the level of cross-correlation. The results indicated higher persistence in the volatility series and two regimes with antipersistence for larger scales in the return series. Cross-correlations suggest that price fluctuations of the leading export variety (Tommy Atkins) have a greater impact on prices in the domestic market (Palmer variety). The cross-correlation coefficient pointed to a stronger correlation between the return series.