In this paper we present some nonlinear autoregressive moving average (NARMA) models proposed in the literature focusing then the attention on the Threshold ARMA (TARMA) models with exogenous threshold variable. The main features of this stochastic structure are shortly discussed and the forecasts generation is presented. It is widely known that in presence of most economic time series the nonlinearity of the data generating process can be well caught by the threshold model under analysis even if, at the same time, the forecast accuracy is not always equally encouraging. Starting from this statement we evaluate how the forecast accuracy of the US Consumer Price Index can be improved when a TARMA model with exogenous threshold variable is fitted to the data. We give empirical evidence that predictors based on a squared loss function can be more accurate when the spread between US Treasury Bonds and US Treasury Bills is selected as threshold variable.
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