Prediction, outliers and autoregressive conditional heteroskedasticity

This thesis studies three related topics in financial econometrics: The estimation and inference from ARCH (Autoregressive Conditional Heteroskedasticity) models in the presence of outliers, the prediction procedures employed with these ARCH models, and other financial measures of risk.; The first topic shows the effect that outliers have on the estimation and inference for ARCH models. We propose for a wide class of ARCH models, an empirically tractable solution to this problem by replacing outliers with their conditional expectations (optimal forecasts) in the likelihood function. This solution works well in both simulations and applications. We demonstrate the accuracy of the procedure for parameter estimation, forecasting, and asset pricing. In addition, we offer a robust bootstrap test for outliers.; The second topic is on the construction of prediction intervals for ARCH models using the bootstrap. We use both a parametric and non-parametric bootstrap, which take account of parameter uncertainty. We compare our prediction intervals to traditional asymptotic prediction intervals, and find that the bootstrap leads to improved accuracy. The accuracy of the bootstrap is empirically demonstrated with the Yen/{dollar}US exchange rate.; The final topic is on Value at Risk (VaR). VaR has been increasingly accepted by both risk managers and regulators as a tool to identify and control exposure to market risk. We introduce a distinction between the structural sources of VaR, and the reduced-form VaR measures that are actually calculated by financial firms. For instance, modern portfolios are characterized by a constantly changing composition of security holdings that reflect portfolio managers' strategies, expected prices, and net cash flows into the portfolio. The distribution of portfolio returns is heterogeneous over time as a result of these time-varying structural factors, which are unlikely to be well-approximated by conventional time-series models. The gap between the structural statistical model and reduced-form measures suggests that these calculations are unreliable and will fail. We formalize the complex evolution of a portfolio, and relate this to standard VaR calculations. The difficulties with these calculations are illustrated in an empirical example consisting of a representative fund manager who is subject to stochastic net cash flows.