A Functional Approach to Test Trending Volatility

Abstract

In this paper 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, pork, poultry and beef products for three different time periods that implied changes in price regulations and behavior. The proposed model seems to adequately fit the volatility process and, according to homoscedasticity tests, outperforms the ARCH(1) and GARCH(1,1) models, some of the most popular approaches used in the literature to analyze price volatility.