Specifi…cation and Testing of Multiplicative Time-Varying GARCH Models with Applications

This paper develops a specification technique for building multiplicative time-varying GARCH models of Amado and Teräsvirta (2011). The model decomposes the variance into an unconditional and conditional components such that the unconditional variance is allowed to evolve smoothly over time. The 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 applying 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 Monte Carlo simulations. The modelling strategy is illustrated in practice with two real examples, an empirical application to daily commodity returns and another one to daily exchange rate returns.