Testing parametric assumptions of trends of a nonstationary time series

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Inference of time-varying regression models (2012, methodology): “6) is a multivariate generalization of Theorem A1 in [54] by using Propositions A.”
Model checking for parametric single‐index models: a dimension reduction model‐adaptive approach (2016, background): “Zhang and Wu (2011), Lin et al. (2014) and Lahaye and Shaw (2014) worked on tests of parametric functional form in non-stationary time series, fixed effects panel data models and heterogeneous auto-regressive models respectively.”