Specification and testing of multiplicative time-varying GARCH models with applications

In this article, we develop a specification technique for building multiplicative time-varying GARCH models of Amado and Teräsvirta (2008, 2013). The variance is decomposed into an unconditional and a conditional component such that the unconditional variance component is allowed to evolve smoothly over time. This nonstationary component is defined as a linear combination of logistic transition functions with time as the transition variable. The appropriate number of transition functions is determined by a sequence of specification tests. For that purpose, a coherent modelling strategy based on statistical inference is presented. It is heavily dependent on Lagrange multiplier type misspecification tests. The tests are easily implemented as they are entirely based on auxiliary regressions. Finite-sample properties of the strategy and tests are examined by simulation. The modelling strategy is illustrated in practice with two real examples: an empirical application to daily exchange rate returns and another one to daily coffee futures returns.This work has been supported by CREATES – Center for Research in Econometric Analysis of Time Series (DNRF78), funded by the Danish National Research Foundation. The first author would also like to acknowledge financial support from the Danish Council for Independent Research (Grant No. 12-126018), from the European Regional Development Fund (ERDF) through the Operational Program Factors of Competitiveness (COMPETE); and by national funds received through FCT – Portuguese Foundation for Science and Technology (Grant No. PTDC/IIM-FIN/4685/2012).FCT Fundação para a Ciência e Tecnologia (COMPETE 2020, PORTUGAL 2020, FEDER