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" Essays on estimation and inference in high-dimensional models with applications to finance and economics "
Zhu, Yinchu
Timmermann, Allan
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Latin Dissertation
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English
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898500
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TL68n8c6pv
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Zhang, Meng
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Essays on estimation and inference in high-dimensional models with applications to finance and economics\ Zhu, YinchuTimmermann, Allan
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2017
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2017
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| Abstract
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Economic modeling in a data-rich environment is often challenging. To allow for enough flexibility and to model heterogeneity, models might have parameters with dimensionality growing with (or even much larger than) the sample size of the data. Learning these high-dimensional parameters requires new methodologies and theories. We consider three important high-dimensional models and propose novel methods for estimation and inference. Empirical applications in economics and finance are also studied. In Chapter 1, we consider high-dimensional panel data models (large cross sections and long time horizons) with interactive fixed effects and allow the covariate/slope coefficients to vary over time without any restrictions. The parameter of interest is the vector that contains all the covariate effects across time. This vector has dimensionality tending to infinity, potentially much faster than the cross-sectional sample size. We develop methods for the estimation and inference of this high-dimensional vector, i.e., the entire trajectory of time variation in covariate effects. We show that both the consistency of our estimator and the asymptotic accuracy of the proposed inference procedure hold uniformly in time. Our methodology can be applied to several important issues in econometrics, such as constructing confidence bands for the entire path of covariate coefficients across time, testing the time-invariance of slope coefficients and estimation and inference of patterns of time variations, including structural breaks and regime switching. An important feature of our method is that it provides inference procedures for the time variation in pre-specified components of slope coefficients while allowing for arbitrary time variation in other components. Computationally, our procedures do not require any numerical optimization and are very simple to implement. Monte Carlo simulations demonstrate favorable properties of our methods in finite samples. We illustrate our methods through empirical applications in finance and economics. In Chapter 2, we consider large factor models with unobserved factors. We formalize the notion of common factors between different groups of variables and propose to use it as a general approach to study the structure of factors, i.e., which factors drive which variables. The spanning hypothesis, which states that factors driving one group are spanned by those driving another group, can be studied as a special case under our framework. We develop a statistical procedure for testing the number of common factors. Our inference procedure is built upon recent results on high-dimensional bootstrap and is shown to be valid under the asymptotic framework of large
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Zhu, Yinchu
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UC San Diego
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