The　radial　basis　function　network-based　state-dependent　autoregressive　(RBF-AR)　model　has　been　widely　used　in　modeling　and　prediction　of　nonlinear　time　series.　The　parameter　identification　of　RBF-AR　model　can　be　reformulated　as　a　separable　nonlinear　least　squares　problem.　The　variable　projection　(VP)　algorithm　has　been　proven　to　be　valuable　in　solving　such　problems.　However,　for　ill-posed　problems,　the　classical　VP　algorithm　usually　yields　unstable　models.　In　this　paper,　we　consider　a　novel　regularized　separable　algorithm　that　takes　advantage　of　the　VP　method　and　the　expectation–maximization　(EM)　method.　The　proposed　algorithm　utilizes　the　VP　algorithm　to　optimize　the　nonlinear　parameters　and　automatically　picks　out　the　regularization　parameters　during　the　search　process.　Numerical　results　on　real-world　data　and　synthetic　time　series　confirm　the　effectiveness　of　the　proposed　algorithm.　©　2021,　The　Author(s),　under　exclusive　licence　to　Springer　Nature　B.V.