In this paper, we present a new time series model, whichdescribes self-exciting threshold autoregressive (SETAR) nonlinearityand seasonality simultaneously. The model is termed multiplicativeseasonal SETAR (SEASETAR). It can be viewed as a special case of ageneral non-multiplicativeSETAR model by imposing certain restrictions on the parameters of thelatter model. Related to these restrictions, we introduce twoC(alpha)-type test statistics, one deals with gaps, and the othertests for multiplicative constraints in non-multiplicative SETARmodels.These statistics form the basis of a new seasonality-test. We alsopresent a model selection strategy. The usefulness of bothnon-multiplicative SETAR model and multiplicative SEASETAR models isexamined by applying these models to five monthly series of inflationrates. It turns out that the test statistics mentionedabove play an important role in finding the best model for theseries.Also, the estimated models can be sensibly interpreted from aneconomicstandpoint. Finally, to get a better understanding of the basicfeatures underlying the fitted SEASETAR models a dynamic analysis iscarried out. The results of this analysis can be used to generatemorerealistic future scenarios of outcomes in order to settle solvencymargins in the insurance business.