Nonlinear stochastic inflation modelling using SEASETARs

The development of stochastic inflation models for actuarial and investment applications has become an important topic to actuaries since Wilkie [Transactions of the Faculty of Actuaries 39 (1986) 341] introduced his first investment model. Two empirical features of monthly inflation rates are dynamic dependence on the level of the series and seasonal fluctuations. We propose a model, termed multiplicative seasonal self-exciting threshold autoregressive (SEASETAR), which captures both features simultaneously. The model is a special case of a general non-multiplicative SETAR model. The usefulness of multiplicative SEASETAR models is demonstrated by analyzing five data series of monthly inflation rates. One of these series corresponds to a country with hyperinflation episodes. To get a better understanding of the basic features underlying the fitted SEASETAR models we also perform a dynamic analysis.