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Title: Testing of parametric additive time-varying GARCH models Authors:  Niklas Ahlgren - Hanken School of Economics (Finland) [presenting]
Alexander Back - Hanken School of Economics (Finland)
Timo Terasvirta - Aarhus University (Denmark)
Abstract: The aim is twofold. First, it develops a specification test for GARCH models with a time-varying intercept. The time-varying intercept is modelled by logistic transition functions with rescaled time as the transition variable. The model is an example of an additive decomposition of the conditional variance such that the conditional variance component is allowed to evolve smoothly over time. The model is called an additive time-varying (ATV-)GARCH model. The ATV-GARCH model is globally nonstationary but locally stationary. We derive Lagrange multiplier (LM) tests of GARCH against ATV-GARCH. The tests are based on auxiliary regressions. Despite the non-stationarity of the process, the LM statistics have standard asymptotic null distributions. The finite-sample properties of the tests are examined by simulations. Second, the article discusses a modelling strategy for ATV- and multiplicative time-varying (MTV-)GARCH models. The LM tests against ATV and MTV alternatives are not asymptotically independent and have power against each other. Both models accommodate deterministic changes in the amplitude of volatility clusters and the unconditional variance. The choice between these two types of models is an empirical question. A computational advantage of the additive model is that it is simpler to fit than the multiplicative model. The testing-based modelling strategy is illustrated by two empirical examples.