Spurious functional-coefficient regression models and robust inference with marginal integration

Functional-coefficient cointegrating models have become popular to model nonlinear nonstationarity in econometrics (Cai et al., 2009; Xiao, 2009). However, there is rare study on testing the existence of functional-coefficient cointegration. Consequently, functional-coefficient regressions involving nonstationary regressors may be spurious. This paper investigates the effect that spurious functional-coefficient regression has on the model diagnostics. We find that common characteristics of spurious regressions are manifest, including divergent local significance tests, random local goodness-of-fit, and local Durbin–Watson ratio converging to zero, complementing those discovered in spurious linear and nonparametric regressions (Phillips, 1986, 2009). In addition, spuriousness causes the divergences of the global significance tests proposed by Xiao (2009) and Sun et al. (2016), which are likely to produce misleading conclusions for practitioners when cointegration tests fail to reject a spurious regression. To resolve the problems, we propose a simple-to-implement inference procedure based on a semiparametric balanced regression, by augmenting regressors of the original spurious regression with lagged dependent variable and independent variables, with the aid of the marginal integration. This procedure achieves spurious regression detection via standard nonparametric inferential asymptotics, and is found robust to the true relationship between the integrated processes. The theoretical results are also corroborated by simulations.