We　propose,　in　this　paper,　a　framework　for　time　series　and　nonlinear　system　modeling,　called　the　basis　function　matrix-based　flexible　coefficient　autoregressive　(BFM-FCAR)　model.　It　has　very　flexible　nonlinear　structure.　We　show　that　many　famous　nonlinear　time　series　models　can　be　derived　under　this　framework　by　choosing　the　proper　basis　function　matrices.　Some　probabilistic　properties　(the　conditions　of　geometrical　ergodicity)　of　the　BFM-FCAR　model　are　investigated.　Taking　advantage　of　the　model　structure,　we　present　an　efficient　parameter　estimation　algorithm　for　the　proposed　framework　by　using　the　variable　projection　method.　Finally,　we　show　how　new　models　are　generated　from　the　proposed　framework.　©　2013　IEEE.