Inference for nonparametric high-frequency estimators with an application to time variation in betas

We consider the problem of conducting inference on nonparametric high-frequency estimators without knowing their asymptotic variances. We prove that a multivariate subsampling method achieves this goal under general conditions that were not previously available in the literature. We suggest a procedure for a data-driven choice of the bandwidth parameters. Our simulation study indicates that the subsampling method is much more robust than the plug-in method based on the asymptotic expression for the variance. Importantly, the subsampling method reliably estimates the variability of the Two Scale estimator even when its parameters are chosen to minimize the finite sample Mean Squared Error; in contrast, the plugin estimator substantially underestimates the sampling uncertainty. By construction, the subsampling method delivers estimates of the variance-covariance matrices that are always positive semi-definite. We use the subsampling method to study the dynamics of financial betas of six stocks on the NYSE. We document significant variation in betas within year 2006, and find that tick data captures more variation in betas than the data sampled at moderate frequencies such as every five or twenty minutes. To capture this variation we estimate a simple dynamic model for betas. The variance estimation is also important for the correction of the errors-in-variables bias in such models. We find that the bias corrections are substantial, and that betas are more persistent than the naive estimators would lead one to believe.

Aufklärung et limitation du possible

Le thème de l’émergence de la Raison à partir du mythe est central à La dialectique de la Raison et à l’entreprise générale de l’École de Francfort. C’est que ce qui s’annonçait comme une libération par rapport à la pensée mythique et à la domination justifiée par celle-ci s’est retourné : la liberté vis-à-vis de l’arbitraire de la nature s’est payé d’un asservissement plus grand encore. Et, à son sommet, la raison a fini par replonger dans le mythe. Dans cet essai, nous proposons, en suivant Adorno, une analyse de cette «nouvelle domination» en montrant de quelle façon l’Aufklärung est venue restreindre le champ de la possibilité. Cela appelle à penser la domination non pas comme une simple imposition hétéronome, mais, plus fondamentalement, comme un étouffement du possible.