Linearity and misspecification tests for vector smooth transition regression models

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Specification, estimation and evaluation of vector smooth transition autoregressive models with applications (2014, methodology): “Linearity and misspecification tests when a single transition variable is controlling the transition in the whole system need special consideration and are discussed in Teräsvirta and Yang (2014).”
THRESHOLDS AND SMOOTH TRANSITIONS IN VECTOR AUTOREGRESSIVE MODELS (2013, background): “where Δyt is I(0), AjB0; j= 1; 2; are reduced rank m×m matrices as in Eq. (14) and Gðγ; c; stÞ is a diagonal matrix defined in Eq. (17). Rothman, van Dijk, and Franses (2001) defined the STVEC model assuming Gðγ; c; stÞ=Gðγ; c; stÞIm: Camacho (2004) constructed a two-dimensional (m1⁄4 2) STVEC model”