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.区间时间序列（Interval Time Series, ITS）分析在计量经济分析中具有重要意义，因其包含经济过程的变动幅度、水平或趋势相关信息。尤为关键的是，区间数据所承载的丰富信息可用于实现更为精准的定量估计与统计推断。考虑到区间时间序列数据可能存在的非线性特征，本文提出一类平滑转换区间自回归（smooth transition interval autoregressive, STIAR）模型，其中逻辑斯蒂STIAR（LSTIAR）模型与指数STIAR（ESTIAR）模型均为其特例。本文提出最小距离估计法对模型参数进行估计，并构建了对应估计量的渐近理论，同时模型的非线性检验问题也得到了妥善解决。文末给出了若干数值模拟结果与一则实际数据案例。