On Smooth Transition Interval Autoregressive Models

Interval time series (ITS) analysis has important significance econometric analysis, as it contains information about the range of change and the level or trend of economic processes. More importantly, the rich information of interval data can be used for more accurate quantitative estimation and inference. Considering the possible nonlinear characteristics of ITS data, this article introduces a class of smooth transition interval autoregressive (STIAR) models, which includes the logistic STIAR (LSTIAR) model and the exponential STIAR (ESTIAR) model as special cases. The minimum distance estimation method is proposed to estimate the model parameters and the asymptotic theory of the estimator is established. The nonlinearity test of the model is also well solved. Finally, some numerical simulation results and a practical data example are given.