On the least squares estimation of multiple-regime threshold autoregressive models

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STRUCTURAL THRESHOLD REGRESSION (2016, unknown): “More recently, in the context of the multiple-regime threshold autoregressive model, Li and Ling (2012) revisit the theory of Chan and propose a numerical approach to simulate the limiting distribution of the estimated threshold based on a simulation of a related compound Poisson process.”
Hysteretic autoregressive time series models (2015, methodology): “Theorem 4 can be obtained by combining the methods of proof for Theorem 3.3 in Li & Ling (2012) and Theorem 2.3 in Li et al. (2013).”
Bootstrap prediction intervals for linear, nonlinear, and nonparametric autoregressions (2016, background): “If the threshold C is unknown, it can be estimated (also via LS) at a rate that is faster than √ n so that the limit distribution of the LS estimators remains unaffected; see Li and Ling (2012) [25] and the references therein.”
Nested sub-sample search algorithm for estimation of threshold models (2016, methodology): “This issue has been commonly tackled by using the single grid search (SGS) algorithm over a feasible threshold space; see Tong and Lim (1980), Chan (1993), Hansen (1997, 2000), Gonzalo and Pitarakis (2002), Li and Ling (2012), Yu (2012), and others.”