Modelling Seasonalities in Nonlinear Inflation Rates using SEASETARs

In this paper, we present a new time series model, which describes self-exciting threshold autoregressive (SETAR) nonlinearity and seasonality simultaneously. The model is termed multiplicative seasonal SETAR (SEASETAR). It can be viewed as a special case of a general non-multiplicative SETAR model by imposing certain restrictions on the parameters of the latter model. Related to these restrictions, we introduce two C(®)-type test statistics, one deals with gaps, and the other tests for multiplicative constraints in non-multiplicative SETAR models. These statistics form the basis of a new seasonality-test. We also present a model selection strategy. The usefulness of both non-multiplicative SETAR model and multiplicative SEASETAR models is examined by applying these models to ̄ve monthly series of in°ation rates. It turns out that the test statistics mentioned above play an important role in ̄nding the best model for the series. Also, the estimated models can be sensibly interpreted from an economic standpoint. Finally, to get a better understanding of the basic features underlying the ̄tted SEASETAR models a dynamic analysis is carried out. The results of this analysis can be used to generate more realistic future scenarios of outcomes in order to settle solvency margins in the insurance business.