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Statistical Inferences on High-Frequency Financial Data and Quantum State Tomography.

Record Type:	Language materials, manuscript : Monograph/item
Title/Author:	Statistical Inferences on High-Frequency Financial Data and Quantum State Tomography./
Author:	Kim, Donggyu.
Description:	1 online resource (382 pages)
Notes:	Source: Dissertation Abstracts International, Volume: 77-12(E), Section: B.
Contained By:	Dissertation Abstracts International77-12B(E).
Subject:	Statistics. -
Online resource:	click for full text (PQDT)
ISBN:	9781369025798

Statistical Inferences on High-Frequency Financial Data and Quantum State Tomography.
Kim, Donggyu.

Statistical Inferences on High-Frequency Financial Data and Quantum State Tomography. - 1 online resource (382 pages)

Source: Dissertation Abstracts International, Volume: 77-12(E), Section: B.

Thesis (Ph.D.)

Includes bibliographical references

In this dissertation, we study two topics, the volatility analysis based on the high-frequency financial data and quantum state tomography.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2018

Mode of access: World Wide Web

ISBN: 9781369025798Subjects--Topical Terms:

556824
Statistics.
Index Terms--Genre/Form:

554714
Electronic books.

Statistical Inferences on High-Frequency Financial Data and Quantum State Tomography.
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099 $a TUL $f hyy $c available through World Wide Web
100 1 $a Kim, Donggyu. $3 1179088
245 1 0 $a Statistical Inferences on High-Frequency Financial Data and Quantum State Tomography.
264 0 $c 2016
300 $a 1 online resource (382 pages)
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
500 $a Source: Dissertation Abstracts International, Volume: 77-12(E), Section: B.
500 $a Adviser: Yazhen Wang.
502 $a Thesis (Ph.D.) $c The University of Wisconsin - Madison $d 2016.
504 $a Includes bibliographical references
520 $a In this dissertation, we study two topics, the volatility analysis based on the high-frequency financial data and quantum state tomography.
520 $a In Part I, we study the volatility analysis based on the high-frequency financial data. We first investigate how to estimate large volatility matrices effectively and efficiently. For example, we introduce threshold rules to regularize kernel realized volatility, pre-averaging realized volatility, and multi-scale realized volatility. Their convergence rates are derived under sparsity on the large integrated volatility matrix. To account for the sparse structure well, we employ the factor-based Ito processes and under the proposed factor-based model, we develop an estimation scheme called "blocking and regularizing". Also, we establish a minimax lower bound for the eigenspace estimation problem and propose sparse principal subspace estimation methods by using the multi-scale realized volatility matrix estimator or the pre-averaging realized volatility matrix estimator. Finally, we introduce a unified model, which can accommodate both continuous-time Ito processes used to model high-frequency stock prices and GARCH processes employed to model low-frequency stock prices, by embedding a discrete-time GARCH volatility in its continuous-time instantaneous volatility. We adopt realized volatility estimators based on high-frequency financial data and the quasi-likelihood function for the low-frequency GARCH structure to develop parameter estimation methods for the combined high-frequency and low-frequency data.
520 $a In Part II, we study the quantum state tomography with Pauli measurements. In the quantum science, the dimension of the quantum density matrix usually grows exponentially with the size of the quantum system, and thus it is important to develop effective and efficient estimation methods for the large quantum density matrices. We study large density matrix estimation methods and obtain the minimax lower bound under some sparse structures, for example, (i) the coefficients of the density matrix with respect to the Pauli basis are sparse; (ii) the rank is low; (iii) the eigenvectors are sparse. Their performances may depend on the sparse structure, and so it is essential to choose appropriate estimation methods according to the sparse structure. In light of this, we study how to conduct hypothesis tests for the sparse structure. Specifically, we propose hypothesis test procedures and develop central limit theorems for each test statistics. A simulation study is conducted to check the finite sample performances of proposed estimation methods and hypothesis tests.
533 $a Electronic reproduction. $b Ann Arbor, Mich. : $c ProQuest, $d 2018
538 $a Mode of access: World Wide Web
650 4 $a Statistics. $3 556824
650 4 $a Finance. $3 559073
650 4 $a Quantum physics. $3 1179090
655 7 $a Electronic books. $2 local $3 554714
690 $a 0463
690 $a 0508
690 $a 0599
710 2 $a ProQuest Information and Learning Co. $3 1178819
710 2 $a The University of Wisconsin - Madison. $b Statistics. $3 1179089
773 0 $t Dissertation Abstracts International $g 77-12B(E).
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10147354 $z click for full text (PQDT)