Uncertainty And Learning In Dynamic Financial Econometrics

Every day the news reminds us that we live in a complex, ever-changing world. Against that background, this dissertation studies the econometrics of the interaction between time-varying uncertainty and learning. In particular, it develops parsimonious nonparametric methods for estimating risk in real time. The first two chapters develop tractable models and estimators for entire densities. The third chapter provides identification-robust inference for the prices of market and volatility risk when volatility exhibits complex dynamics. The first chapter, Jumps, Realized Densities, and News Premia, studies how jumps affect asset prices. It derives both a tractable nonparametric continuous-time representation for the price jumps and an implied sufficient statistic for their dynamics. This statistic — jump volatility — is the instantaneous variance of the jump part and measures news risk. It also develops estimators for the volatilities and nonparametrically identifies continuous-time jump dynamics and associated risk premia. It also provides a detailed empirical application to the S&P 500, showing that the jump volatility commands a smaller premium than the diffusion volatility does. The second chapter, Bypassing the Curse of Dimensionality: Feasible Multivariate Density Estimation, is coauthored with Minsu Chang and studies nonparametrically estimating multivariate densities. Most economic data are multivariate and estimating their densities is a classic problem. However, the curse of dimensionality makes nonparametrically estimating the data’s density infeasible when there are many series. This chapter does not seek to provide estimators that perform well all of the time (it is impossible) but instead adapts ideas from the Bayesian compression literature to provide estimators that perform well most of the time. The third chapter, Identification-Robust Inference for Risk Prices in Structural Stochastic Volatility Models, is coauthored with Xu Cheng and Eric Renault and studies the identification problems inherent to measuring compensation for risk in stochastic volatility asset pricing models. Disentangling the channels by which risk affects expected returns is difficult and poses a subtle identification problem that invalidates standard inference. We adapt the conditional quasi-likelihood ratio test Andrews and Mikusheva (2016) develop in a GMM framework to a minimum distance framework to provide uniformly valid confidence sets

Discrete quantum geometries and their effective dimension

In several approaches towards a quantum theory of gravity, such as group field theory and loop quantum gravity, quantum states and histories of the geometric degrees of freedom turn out to be based on discrete spacetime. The most pressing issue is then how the smooth geometries of general relativity, expressed in terms of suitable geometric observables, arise from such discrete quantum geometries in some semiclassical and continuum limit. In this thesis I tackle the question of suitable observables focusing on the effective dimension of discrete quantum geometries. For this purpose I give a purely combinatorial description of the discrete structures which these geometries have support on. As a side topic, this allows to present an extension of group field theory to cover the combinatorially larger kinematical state space of loop quantum gravity. Moreover, I introduce a discrete calculus for fields on such fundamentally discrete geometries with a particular focus on the Laplacian. This permits to define the effective-dimension observables for quantum geometries. Analysing various classes of quantum geometries, I find as a general result that the spectral dimension is more sensitive to the underlying combinatorial structure than to the details of the additional geometric data thereon. Semiclassical states in loop quantum gravity approximate the classical geometries they are peaking on rather well and there are no indications for stronger quantum effects. On the other hand, in the context of a more general model of states which are superposition over a large number of complexes, based on analytic solutions, there is a flow of the spectral dimension from the topological dimension $d$ on low energy scales to a real number $0<\alpha<d$ on high energy scales. In the particular case of $\alpha=1$ these results allow to understand the quantum geometry as effectively fractal.Comment: PhD thesis, Humboldt-Universit\"at zu Berlin; urn:nbn:de:kobv:11-100232371; http://edoc.hu-berlin.de/docviews/abstract.php?id=4204

FIBER-OPTIC BUNDLE FLUORESCENCE MICROSCOPY FOR FUNCTIONAL BRAIN ACTIVITY MAPPING

Understanding the relationship between cellular activities in the animal brain and the emerging patterns of animal behavior is a critical step toward completing the Brain Activity Map. This dissertation describes the development of fiber-bundle microscopy capable of high-resolution cellular imaging, for mapping of functional brain activity in freely moving mice. As a part of this work, several fiber-bundle microscope systems and image processing algorithms were proposed and developed. These optical imaging methods and system performance were tested and evaluated by performing in vivo animal brain imaging. Several fiber-bundle imaging devices, including a dual-mode confocal reflectance and fluorescence micro-endoscope, a single ball-lens imaging probe, and a spatially multiplexed fiber-bundle imager, were designed and developed for high-resolution imaging of brain cells and visualization of brain activity. A dual-mode micro-endoscope, simultaneously achieving laser scanning confocal reflectance and fluorescence imaging, was developed to quantitatively assess gene transfection efficacy using human cervical cancer cells. A single ball-lens integrated imaging probe was designed for endoscopic brain imaging. Lastly, a spatially multiplexed fiber-bundle imager that allows concurrent monitoring of astrocytic activities in multiple brain regions and enables optical manipulation with cell-specific targeting was proposed and experimentally demonstrated. Novel image-processing algorithms were used along with the developed imaging systems. Structured illumination employing a digital micro-mirror device (DMD) was integrated into the system to achieve depth-resolved imaging with a wide-field illumination fiber-bundle microscope. Data from super-resolution fiber-bundle microscopy based on the linear structured illumination were numerically processed to extend the lateral resolution beyond the diffraction limit. To evaluate the performance of the developed fiber-bundle microscope systems and image reconstruction algorithms, the systems and methods were each tested and validated on in vivo animal models, namely transgenic mice expressing a genetically encoded Calcium indicator (GCaMP3) within astrocytes. We showed that locomotion triggers simultaneous activation of astrocyte networks in multiple brain regions in mice. We have also demonstrated real-time cellular-resolution dual-color functional brain imaging in mice. Finally, we established a platform that allows real-time and non-invasive imaging of the intact central nervous system of freely behaving mice. Using this platform, we observed, for the first time, physiologically relevant activation of astrocytes during behaviorally relevant tasks and in the natural setting. In addition, we present a proof-of-concept study by using a fiber-bundle ring light-guided portable multispectral imaging (MSI) platform capable of tissue characterization and preoperative surgical planning for intestinal anastomosis