CHRONOLOGICALLY TRIMMED LS FOR NONLINEAR PREDICTIVE REGRESSIONS WITH PERSISTENCE OF UNKNOWN FORM

Relatively, recent work by Jeganathan (2008, Cowles Foundation Discussion Paper 1649) and Wang (2014, Econometric Theory , 30(3), 509–535) on generalized martingale central limit theorems (MCLTs) implicitly introduces a new class of instrument arrays that yield (mixed) Gaussian limit theory irrespective of the persistence level in the data. Motivated by these developments, we propose a new semiparametric method for estimation and inference in nonlinear predictive regressions with persistent predictors. The proposed method that we term chronologically trimmed least squares (CTLS) is comparable to the IVX method of Phillips and Magdalinos (2009, Econometric inference in the vicinity of unity. Mimeo, Singapore Management University) and yields conventional inference in regressions where the nature and extent of persistence in the data are uncertain. In terms of model generality, our contribution to the existing literature is twofold. First, our covariate model space allows for both nearly integrated (NI) and fractional processes (stationary and nonstationary) as a special case, while the vast majority of articles in this area only consider NI arrays. Second, we allow for nonlinear regression functions. The CTLS estimator is obtained by applying certain chronological trimming to the OLS instruments using appropriate kernel functions of time trend variables. In particular, the instruments under consideration are a generalized (averaged) version of those widely used for time-varying parameter (TVP) models. For the purposes of our analysis, we develop a novel asymptotic theory for sample averages of various processes weighted by such kernel functionals which is of independent interest and highly relevant to the TVP literature. Leveraging our nonlinear framework, we also provide an investigation on the effects of misbalancing on the predictability hypothesis. A new methodology is proposed to mitigate misbalancing effects. These methods are used for exploring the predictability of SP500 returns.