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Title: Robust inference for predictive regressions under endogeneity and heteroskedasticity Authors:  Anton Skrobotov - Russian Presidential Academy of National Economy and Public Administration and SPBU (Russia) [presenting]
Rustam Ibragimov - Imperial College London and St. Petersburg State University (United Kingdom)
Jihyun Kim - Indiana University (United States)
Abstract: New simple approaches are proposed to robust inference in predictive regressions. The first approach is based on previous results. First, we utilize instrumental variable estimators such as Cauchy estimator to establish the asymptotic normality of the estimator regardless of the order of integration of the variables in regression models and endogeneity. Second, we show that, under general conditions, robust inference on unknown parameters of interest under heterogeneity and dependence may be conducted by partitioning the data into some number of groups and performing the standard $t$ -test with asymptotically normal parameters group estimates and the critical values of Student-$t$ distributions. The second approach is based on the fact that the limiting volatility process can be estimable as precise as possible asymptotically. Therefore, we can either correct directly the time series using the volatility estimate or use the time change method. These approaches provide standard normal inference in the limit. The proposed approaches to robust inference compare favorably with widely used inference procedures in terms of its finite sample properties and can be used under different general settings with dependence, volatility clustering, heavy tails and potentially nonstationary volatility observed in the real-world financial and economic markets.