ESTIMATION AND INFERENCE IN THE PRESENCE OF FRACTIONAL d=1/2 AND WEAKLY NONSTATIONARY PROCESSES
成果类型：
Article
署名作者：
Duffy, James A.; Kasparis, Ioannis
署名单位：
University of Oxford; University of Cyprus
刊物名称：
ANNALS OF STATISTICS
ISSN/ISSBN：
0090-5364
DOI：
10.1214/20-AOS1998
发表日期：
2021
页码：
1195-1217
关键词：
摘要：
We provide new limit theory for functionals of a general class of processes lying at the boundary between stationarity and nonstationarity-what we term weakly nonstationary processes (WNPs). This includes, as leading examples, fractional processes with d = 1/2, and arrays of autoregressive processes with roots drifting slowly towards unity. We first apply the theory to study inference in parametric and nonparametric regression models involving WNPs as covariates. We then use these results to develop a new specification test for parametric regression models. By construction, our specification test statistic has a chi(2) limiting distribution regardless of the form and extent of persistence of the regressor, implying that a practitioner can validly perform the test using a fixed critical value, while remaining agnostic about the mechanism generating the regressor. Simulation exercises confirm that the test controls size across a wide range of data generating processes, and outperforms a comparable test due to Wang and Phillips (Ann. Statist. 40 (2012) 727-758) against many alternatives.