Using a functional approach to test trending volatility in the price of Mexican and international agricultural products
在GARCH(1,1)模型中引入函数趋势项，分析墨西哥CPI篮子中所有农产品及国际玉米、小麦等价格在三个时期的波动趋势，发现波动趋势先升后降但持续性增强，并指出牛油果、豆类等可能带来短期食品通胀风险。
Abstract In this article, we extend the traditional GARCH(1,1) 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, as well as to the international prices of maize, wheat, swine, poultry, and beef products for three different time periods that implied changes in price regulations and behavior: before the North American Free Trade Agreement (NAFTA; 1987–1993), post‐NAFTA (1994–2005), and commodity supercycle (2006–2014). The proposed model seems to adequately fit the volatility process and, according to heteroscedasticity tests, also outperforms 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 increased from the period 1987–1993 to 1994–2005. From 1994–2005 to 2006–2014, trends decreased but the persistence of volatility increased for most products, especially for international commodities. In addition, we identify some agricultural products such as avocado, beans, and chicken that, due to their increasing price volatility trends in the 2006–2014 period, may present a risk for food inflation in the short run.