This dissertation contains my research results on two topics of nancial econometrics. The rst topic is jump regression where the observation selection procedure can be viewed as the analogy of dimension reduction for the classical big "P" problem in statistics to the big "N" problem in nancial econometrics. The second topic is about estimation and testing of time series models for Value-at-Risk (VaR) and Expected Shortfall (ES), which is the average return on a risky asset conditional on the return being below some quantile of its distribution, namely its VaR. The rst chapter, which is joint work with Jia Li, Viktor Todorov and George Tauchen, develops an ecient mixed-scale estimator for jump regressions using highfrequency asset returns. A novel bootstrap procedure is proposed to make inference about our estimator, which has a non-standard asymptotic distribution that cannot be made asymptotically pivotal via studentization. The Monte Carlo analysis indicates good nite-sample performance of the general specication test and condence intervals based on the bootstrap. When the method is applied to a high-frequency panel of Dow stock prices together with the market index dened by the S&P 500 index futures over the period 2007{2014, we observe remarkable temporal stability in 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 series models for these risk measures. Estimation and inference methods are provided for the proposed models and conrmed via simulation studies to have good nite-sample properties. We apply these models to daily returns on four international equity indices, and nd the proposed new ES-VaR models outperform forecasts based on iv GARCH 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 intractability problem of the asymptotic distribution of the test statistics under the null hypothesis, the subsampling approximation is used to get the asymptotic critical values. A Monte Carlo study shows that the proposed test has better empirical size and power performance in nite samples than other existing tests.
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