Uniform nonparametric series inference for dependent data with an application to the search and matching model

This paper concerns the uniform inference for nonparametric series estimators in time-series applications. We develop a strong approximation theory of sample averages of serially dependent random vectors with dimensions growing with the sample size. The strong approximation is first proved for heterogeneous martingale difference arrays and then extended to general mixingales via martingale approximation, readily accommodating a majority of applications in applied econometrics. We use these results to justify the asymptotic validity of a uniform confidence band for series estimators and show that it can also be used to conduct nonparametric specification test for conditional moment restrictions. The validity of high-dimensional heteroskedasticity and autocorrelation consistent (HAC) estimators is established for making feasible inference. The proposed method is broadly useful for forecast evaluation, empirical microstructure, dynamic stochastic equilibrium models and inference problems based on inter-section bounds. We demonstrate the empirical relevance of the proposed method by studying the Mortensen–Pissarides search and matching model for equilibrium unemployment, and shed new light on the unemployment volatility puzzle from an econometric perspective