Inference in Poorly Identified Econometric Settings with Applications in Financial Economics

Abstract

This dissertation develops several techniques for conducting estimation and inference in non-standard econometric settings. It does so with a particular interest in applying these methods to applications in financial economics. By doing so this dissertation extends the literatures in financial economics and econometrics. The first chapter develops econometric tools for studying the jump dependencies between the underlying or latent spot volatilities of two assets from high-frequency observations on a fixed time interval -- with a particular interest in the relationship between the individual volatilities of traded assets and the volatilities of aggregate risk factors such as the market volatility. The chapter derives an asymptotically valid test for the stability of a linear volatility jump relationship between these assets and proposes an asymptoticly valid and consistent likelihood based estimator for the beta in such relationships. The estimation context is made especially challenging because the error shrinks at a rate much slower than the standard root-n parametric rate. To conduct inference the chapter proposes a bootstrap procedure together with a justification of its asymptotic validity. Finally, the chapter considers three empirical applications of the methods and an extension on how to incorporate a Bayesian prior.The second chapter, which represents joint work with George Tauchen, develops a method to select the threshold in threshold-based jump detection methods. The method is motivated by an analysis of threshold-based jump detection methods in the context of jump-diffusion models. The chapter shows that over the range of sampling frequencies a researcher is most likely to encounter that the usual in-fill asymptotics provide a poor guide for selecting the jump threshold. Because of this we develop a sample-based method. Our method estimates the number of jumps over a grid of thresholds and selects the optimal threshold at what we term the `take-off' point in the estimated number of jumps. The chapter show that this method consistently estimates the jumps and their indices as the sampling interval goes to zero. In several Monte Carlo studies we evaluate the performance of our method based on its ability to accurately locate jumps and its ability to distinguish between true jumps and large diffusive moves. In one of these Monte Carlo studies we evaluate the performance of our method in a jump regression context. Finally, we apply our method in two empirical studies. In one we estimate the number of jumps and report the jump threshold our method selects for three commonly used market indices. In the other empirical application we perform a series of jump regressions using our method to select the jump threshold.The third chapter proposes a model and framework for forecasting the high-frequency analogue of two widely used tail risk measures: the value at risk and the expected shortfall. It does so by using the theory and literature on high-frequency asset price processes to motivate a particular pure-jump semimartingale forecasting model of high-frequency asset returns and thereby high-frequency value at risk and expected shortfall forecasts. Contrasted with methods developed to forecast daily values at risk and expected shortfalls this model provides a substantial improvement in the forecasting of high-frequency expected shortfalls and a modest, although still significant, improvement in the forecasting of high-frequency values at risk. Finally, the fourth chapter develops a method for modeling high-frequency asset prices. It does so by showing how asset prices might be transformed into Levy processes. Once in the class of Levy processes this chapter develops a novel estimation procedure and a novel test of a model's specification by performing the estimation and testing over a suitably chosen family of weighting functions. An empirical study fits a selection of asset returns to two classes of Levy processes; and, finally, a detailed empirical exercise develops a flexible method to calculate intraday values at risk up to any within day horizon. A backtest of the intraday values at risk show their coverage to be right in line with the theoretical correct values.