Essays on Financial Econometrics

Abstract

This dissertation contains my research results on two topics of nancial econometrics.The rst topic is jump regression where the observation selection procedure can beviewed as the analogy of dimension reduction for the classical big "P" problem instatistics to the big "N" problem in nancial econometrics. The second topic is aboutestimation and testing of time series models for Value-at-Risk (VaR) and ExpectedShortfall (ES), which is the average return on a risky asset conditional on the returnbeing below some quantile of its distribution, namely its VaR.The rst chapter, which is joint work with Jia Li, Viktor Todorov and GeorgeTauchen, develops an ecient mixed-scale estimator for jump regressions using highfrequencyasset returns. A novel bootstrap procedure is proposed to make inferenceabout our estimator, which has a non-standard asymptotic distribution that cannotbe made asymptotically pivotal via studentization. The Monte Carlo analysis indicatesgood nite-sample performance of the general specication test and condenceintervals based on the bootstrap. When the method is applied to a high-frequencypanel of Dow stock prices together with the market index dened by the S&P 500index futures over the period 2007{2014, we observe remarkable temporal stabilityin the way that stocks react to market jumps.The second chapter is co-authored with Andrew J. Patton and Johanna F. Ziegel.We use recent results from statistical decision theory to overcome the problem of\elicitability" for ES by jointly modelling ES and VaR, and propose new time seriesmodels for these risk measures. Estimation and inference methods are provided forthe proposed models and conrmed via simulation studies to have good nite-sampleproperties. We apply these models to daily returns on four international equityindices, and nd the proposed new ES-VaR models outperform forecasts based onivGARCH or rolling window models.The third chapter is my single-authored paper which proposes a consistent speci-cation test of dynamic joint models for VaR and ES. To overcome the intractabilityproblem of the asymptotic distribution of the test statistics under the null hypothesis,the subsampling approximation is used to get the asymptotic critical values. AMonte Carlo study shows that the proposed test has better empirical size and powerperformance in nite samples than other existing tests.