Using an in-fill argument, the properties of the sample median of a sequence of events are established both for the case of a fixed period of time and for a period which shrinks as the sample size grows.  The results are used to study the properties of the sample median of absolute returns under stochastic volatility.  This estimator is invariant, asymptotically pivotal and a 1/2 breakdown estimator.  In practice it has deep robustness to jump processes even when there are jumps of α-stable type.  

Estimating linear regression using least squares and reporting robust
standard errors is very common in financial economics, and indeed, much of
the social sciences and elsewhere.   For thick tailed predictors under
heteroskedasticity this recipe for inference performs poorly, sometimes
dramatically so. Here, we develop an alternative approach which delivers an
unbiased, consistent and asymptotically normal estimator so long as the
means of the outcome and predictors are finite.  The new method has
standard errors under heteroskedasticity which are easy to reliably estimate
and tests which are close to their nominal size. The procedure works well
in simulations and in an empirical exercise.  An extension is given to
quantile regression.

In panel experiments, we randomly expose multiple units to different interventions and measure their subsequent outcomes, sequentially repeating the procedure numerous times. Using the potential outcomes framework, we define finite population dynamic causal effects that capture the relative effectiveness of alternative treatment paths. For the leading example, known as the lag-p dynamic causal effects, we provide a nonparametric estimator that is unbiased over the randomization distribution. We then derive the finite population limiting distribution of our estimators as either the sample size or the duration of the experiment increases. Our approach provides a new technique for deriving finite population central limit theorems that exploits the underlying Martingale property of unbiased estimators. We further describe two methods for conducting inference on dynamic causal effects: a conservative test for weak null hypotheses of zero average causal effects using the limiting distribution and an exact randomization-based test for sharp null hypotheses. We also derive the finite population limiting distribution of commonly-used linear fixed effects estimators, showing that these estimators perform poorly in the presence of dynamic causal effects. We conclude with a simulation study and an empirical application in which we reanalyze a lab experiment on cooperation.

Estimation of time-varying covariances is a key input in risk management and asset allocation. ARCH-type multivariate models are used widely for this purpose. Estimation of such models is computationally costly and parameter estimates are meaningfully biased when applied to a moderately large number of assets. Here we propose a novel estimation approach that suffers from neither of these issues, even when the number of assets is in the hundreds. The theory of this new method is developed in some detail. The performance of the proposed method is investigated using extensive simulation studies and empirical examples.

Much research and policy attention has been on socio economic gaps in participation at university, but little attention has been paid to gaps in earnings. This paper addresses this shortfall using tax and student loan administrative data to investigate the earnings of English graduates up to their mid thirties by socio economic background. We find that  graduates from higher income families (from the top fth of the income distribution of those enrolled in university) have average earnings which are 20% higher than those from lower income families. Once we condition on institution and subject choices, this premium roughly halves, to around 10%. The premium grows with age and is larger for men, in particular for men at the most selective universities. We follow Chetty et al. (2017) and estimate English mobility scorecards by university and subject, highlighting the good performance of medicine, economics, law, business, engineering, technology, math, computer science and architecture courses as well as the prominent London-based universities.

We define causal estimands for experiments on single time series, extending the potential outcome framework to dealing with temporal data.  Our approach allows the estimation of a broad class of these estimands and exact randomization based p-values for testing causal effects, without imposing stringent assumptions.  We further derive a general central limit theorem that can be used to conduct conservative tests and build confidence intervals for causal effects.  Finally, we provide three methods for generalizing our approach to multiple units that are receiving the same class of treatment, over time.  We test our methodology on simulated "potential autoregressions,"which have a causal interpretation.  Our methodology is partially inspired by data from a large number of experiments carried out by a financial company who compared the impact of two different ways of trading equity futures contracts.  We use our methodology to make causal statements about their trading methods.

We propose a novel Dirichlet-based Pólya tree (D-P tree) prior on the copula and based on the D-P tree prior, a nonparametric Bayesian inference procedure. Through theoretical analysis and simulations, we are able to show that the flexibility of the D-P tree prior ensures its consistency in copula estimation, thus able to detect more subtle and complex copula structures than earlier nonparametric Bayesian models, such as a Gaussian copula mixture. Furthermore, the continuity of the imposed D-P tree prior leads to a more favourable smoothing effect in copula estimation over classic frequentist methods, especially with small sets of observations. We also apply our method to the copula prediction between the S&P 500 index and the IBM stock prices during the 2007–08 financial crisis, finding that D-P tree-based methods enjoy strong robustness and flexibility over classic methods under such irregular market behaviours.