Essays in financial econometrics

This dissertation focuses on robust volatility and Value-at-Risk (VaR) prediction and inference for financial time series. The VaR forecasts addressed in dynamic models typically ignore the issue of parameter estimation. Due to this parameter uncertainty, valuable investment information, such as confidence intervals of VaR, is unavailable. To deal with this problem, this dissertation provides a complete asymptotic theory that demonstrates the uncertainty due to parameter estimation. I also show how to construct asymptotic forecast intervals that incorporate parameter uncertainty in various contexts.;The first essay considers interval estimation of Value-at-Risk (VaR) for autoregressive processes with GARCH-type errors. I characterize the asymptotic distribution of the VaR estimator, and this distribution accounts for uncertainty in both mean and variance estimation. This parameter uncertainty complicates interval estimation of VaR since VaR estimation is based on the estimated residuals instead of the true residuals. Kernel smoothing of the resealed residuals is proposed to improve quantile estimation in terms of a smaller mean squared error. The theory provides confidence bands for widely used Q-Q plots and interval VaR estimation, which are illustrated in an empirical study.;The second essay proposes new robust Value-at-Risk (VaR) forecasts and provides a complete asymptotic theory that acknowledges parameter uncertainty. The proposed forecasts are based on a two-stage procedure that combines nonparametric volatility estimation and residual quantile estimation. Not only do the forecasts reduce volatility misspecification risk, but they are also robust to the presence of heavy-tailed errors. These heavy-tailed errors make existing methods less attractive in terms of slower convergent speeds and unknown asymptotic distributions. In the second stage, a Bahadur representation of the residual based empirical distribution includes an adjustment term that accounts for volatility estimation. The asymptotic variance of the residual quantile estimator is also shown to be affected by parameter uncertainty. Finally, this paper provides the asymptotic theory of the proposed VaR estimators and constructs asymptotic forecast intervals which incorporate parameter uncertainty due to volatility estimation. Simulations show the new VaR prediction methods are robust. A set of market index data is used to illustrate the proposed VaR forecasts.