QRFE Seminar by Jia Li (Singapore Management University)

'Optimal Inference for Spot Regressions' with Tim Bollerslev and Yuexuan Ren

Abstract: 
We propose new nonparametric inference procedures for the continuous-time regression coefficient and the residual variance for Itˆo semi martingale processes. Treating the local estimation window as fixed, we couple the nonparametric estimation problem with a conditional Gaussian limit experiment, establishing asymptotic optimality of the resulting estimators via a novel “spot” version of the Gauss–Markov theorem. Asymptotically valid feasible inference procedures based on the non-Gaussian exact distributions in the limit experiment perform excellently in finite-samples. An empirical application involving three popular ETFs for the Nasdaq-100stock market index reveals non-trivial systematic intraday and episodic deviations from the funds’ stated objectives.