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.　©　2011　IEEE.