The interval autoregressive time series model

This paper mainly suggests a new type of interval time series: interval autoregressive (IAR) model. Firstly we state why we should introduce the interval time series models. Then we give necessary definitions about random intervals and interval time series. Thirdly, we introduce some methods of efficiency evaluation for forecasting of interval time series. And then we discuss parameter estimation and forecasting in IAR model, in which the methods of parameter estimation are based on the evaluation forecasting for interval data. Furthermore, we give the simulation results and apply it to real data from Shanghai Stock Index, which is to illustrate our modeling methodology. This model makes it possible for decision makers to forecast the best and worst possible situations based on interval-valued observations.