Stationarity　is　a　key　tool　in　classical　time　series.　In　order　to　analyze　the　set-valued　time　series,　it　must　be　extended　to　the　set-valued　case.　In　this　paper,　stationary　set-valued　time　series　is　defined　via　D-p　metric　of　set-valued　random　variables.　Then,　estimation　methods　of　expectation　and　auto-covariance　function　of　stationary　set-valued　time　series　are　proposed.　Unbiasedness　and　consistency　of　the　expectation　estimator　and　asymptotic　unbiasedness　of　the　auto-covariance　function　estimator　are　justified.　After　that,　a　special　case　of　the　set-valued　time　series,　known　as　interval-valued　time　series,　is　considered.　Two　forecast　methods　of　the　stationary　interval-valued　time　series　are　explicitly　presented.　Furthermore,　the　interval-valued　time　series　is　contextualized　in　the　Box-Jenkins　framework:　an　interval-valued　autoregression　model,　along　with　its　parameter　estimation　method,　is　introduced.　Finally,　experiments　on　both　simulated　and　real　data　are　presented　to　justify　the　efficiency　of　the　parameters　estimation　method　and　the　availability　of　the　proposed　model.　(C)　2015　Elsevier　Inc.　All　rights　reserved.