A Functional Approach to Test Trending Volatility: Evidence of Trending Volatility in the Price of Mexican Agricultural Products

In this paper we extend the traditional ARCH(1) model by including a functional trend term in the conditional volatility of a time series. We derive the main properties of the model and apply it to all agricultural commodities in the Mexican CPI basket for three different time periods that implied changes in price regulations an behavior: pre-NAFTA (1987-1993), post-NAFTA (1994-2005)and commodity supercycle (2006-2014). The proposed model seems to adequately fit the volatility process and also outperforms, in the short run, the ARCH(1) and GARCH(1,1) models, some of the most popular approaches used in the literature to analyze price volatility. Our results show that, consistent with anecdotal evidence, price volatility trends of fruits and vegetables increased from the period 1987-1993 to 1994-2005, whereas they decreased for livestock products. From 1994-2005 to 2006-2014, fruits and vegetable trends decreased, whereas they increased for livestock products. Additionally, we identify some agricultural products that, due to their increasing price volatility trends, may present a risk for food inflation in the short run.