Download or read book Functional Data Based Inference for High Frequency Financial Data written by Bahaeddine Taoufik and published by . This book was released on 2016 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis is concerned with developing new functional data techniques for high frequency financial applications. Chapter 1 of the thesis introduces Functional Data Analysis (FDA) with examples of application to real data. In this chapter, we provide some theoretical foundations for FDA. We also present a general theory and basic properties of reproducing kernel Hilbert spaces (RKHS). Chapter 2 of the thesis explores the relationship between market returns and a number of financial factors by fitting functional regression models. We establish two estimation procedures based on the least squares and generalized least squares methods. We also present four hypothesis testing procedures on the functional regression coefficients based on the squared integral $L^2$ approach and the PCA approach for both least squares and generalized least squares methods. New asymptotic results are established allowing for minor departures from stationarity, to ensure convergence and asymptotic normality of our estimates. Our functional regression model is applied to cross-section returns data. Our data application results indicate a positive correlation between the volatility factor ``FVIX" and the higher returns and a negative correlation between the volatility factor ``FVIX" and the low and middle returns.Chapter 3 of the thesis develops a nonlinear function-on-function model using RKHS for real-valued functions. We establish the minimax rate of convergence of the excess prediction risk. Our simulation studies faced computational challenges due to the complexity of the estimation procedure. We examine the prediction performance accuracy of our model through a simulation study. Our nonlinear function-function model is applied to Cumulative intraday return (CIDR) data in order to investigate the prediction performance of Standard \& Poor's 500 Index (S\&P 500) and the Dow Jones Industrial Average (DJIA) for General Electric Company (GE) and International Business Machines Corp.(IBM) for the three periods defining the crisis: ``Before," `` During," and `` After''.

Download or read book High Frequency Financial Econometrics written by Yacine Aït-Sahalia and published by Princeton University Press. This book was released on 2014-07-21 with total page 683 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive introduction to the statistical and econometric methods for analyzing high-frequency financial data High-frequency trading is an algorithm-based computerized trading practice that allows firms to trade stocks in milliseconds. Over the last fifteen years, the use of statistical and econometric methods for analyzing high-frequency financial data has grown exponentially. This growth has been driven by the increasing availability of such data, the technological advancements that make high-frequency trading strategies possible, and the need of practitioners to analyze these data. This comprehensive book introduces readers to these emerging methods and tools of analysis. Yacine Aït-Sahalia and Jean Jacod cover the mathematical foundations of stochastic processes, describe the primary characteristics of high-frequency financial data, and present the asymptotic concepts that their analysis relies on. Aït-Sahalia and Jacod also deal with estimation of the volatility portion of the model, including methods that are robust to market microstructure noise, and address estimation and testing questions involving the jump part of the model. As they demonstrate, the practical importance and relevance of jumps in financial data are universally recognized, but only recently have econometric methods become available to rigorously analyze jump processes. Aït-Sahalia and Jacod approach high-frequency econometrics with a distinct focus on the financial side of matters while maintaining technical rigor, which makes this book invaluable to researchers and practitioners alike.

Download or read book Handbook of Modeling High Frequency Data in Finance written by Frederi G. Viens and published by John Wiley & Sons. This book was released on 2011-12-20 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: CUTTING-EDGE DEVELOPMENTS IN HIGH-FREQUENCY FINANCIAL ECONOMETRICS In recent years, the availability of high-frequency data and advances in computing have allowed financial practitioners to design systems that can handle and analyze this information. Handbook of Modeling High-Frequency Data in Finance addresses the many theoretical and practical questions raised by the nature and intrinsic properties of this data. A one-stop compilation of empirical and analytical research, this handbook explores data sampled with high-frequency finance in financial engineering, statistics, and the modern financial business arena. Every chapter uses real-world examples to present new, original, and relevant topics that relate to newly evolving discoveries in high-frequency finance, such as: Designing new methodology to discover elasticity and plasticity of price evolution Constructing microstructure simulation models Calculation of option prices in the presence of jumps and transaction costs Using boosting for financial analysis and trading The handbook motivates practitioners to apply high-frequency finance to real-world situations by including exclusive topics such as risk measurement and management, UHF data, microstructure, dynamic multi-period optimization, mortgage data models, hybrid Monte Carlo, retirement, trading systems and forecasting, pricing, and boosting. The diverse topics and viewpoints presented in each chapter ensure that readers are supplied with a wide treatment of practical methods. Handbook of Modeling High-Frequency Data in Finance is an essential reference for academics and practitioners in finance, business, and econometrics who work with high-frequency data in their everyday work. It also serves as a supplement for risk management and high-frequency finance courses at the upper-undergraduate and graduate levels.

Download or read book Inference for Functional Data with Applications written by Lajos Horváth and published by Springer Science & Business Media. This book was released on 2012-05-08 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents recently developed statistical methods and theory required for the application of the tools of functional data analysis to problems arising in geosciences, finance, economics and biology. It is concerned with inference based on second order statistics, especially those related to the functional principal component analysis. While it covers inference for independent and identically distributed functional data, its distinguishing feature is an in depth coverage of dependent functional data structures, including functional time series and spatially indexed functions. Specific inferential problems studied include two sample inference, change point analysis, tests for dependence in data and model residuals and functional prediction. All procedures are described algorithmically, illustrated on simulated and real data sets, and supported by a complete asymptotic theory. The book can be read at two levels. Readers interested primarily in methodology will find detailed descriptions of the methods and examples of their application. Researchers interested also in mathematical foundations will find carefully developed theory. The organization of the chapters makes it easy for the reader to choose an appropriate focus. The book introduces the requisite, and frequently used, Hilbert space formalism in a systematic manner. This will be useful to graduate or advanced undergraduate students seeking a self-contained introduction to the subject. Advanced researchers will find novel asymptotic arguments.

Download or read book Modelling and Forecasting High Frequency Financial Data written by Stavros Degiannakis and published by Springer. This book was released on 2016-04-29 with total page 301 pages. Available in PDF, EPUB and Kindle. Book excerpt: The global financial crisis has reopened discussion surrounding the use of appropriate theoretical financial frameworks to reflect the current economic climate. There is a need for more sophisticated analytical concepts which take into account current quantitative changes and unprecedented turbulence in the financial markets. This book provides a comprehensive guide to the quantitative analysis of high frequency financial data in the light of current events and contemporary issues, using the latest empirical research and theory. It highlights and explains the shortcomings of theoretical frameworks and provides an explanation of high-frequency theory, emphasising ways in which to critically apply this knowledge within a financial context. Modelling and Forecasting High Frequency Financial Data combines traditional and updated theories and applies them to real-world financial market situations. It will be a valuable and accessible resource for anyone wishing to understand quantitative analysis and modelling in current financial markets.

Download or read book Statistical Inferences on High frequency Financial Data and Quantum State Tomography written by Donggyu Kim and published by . This book was released on 2016 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this dissertation, we study two topics, the volatility analysis based on the high-frequency financial data and quantum state tomography. 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 Itô 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 Itô 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. 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.

Download or read book Econometrics of Financial High Frequency Data written by Nikolaus Hautsch and published by Springer Science & Business Media. This book was released on 2011-10-12 with total page 381 pages. Available in PDF, EPUB and Kindle. Book excerpt: The availability of financial data recorded on high-frequency level has inspired a research area which over the last decade emerged to a major area in econometrics and statistics. The growing popularity of high-frequency econometrics is driven by technological progress in trading systems and an increasing importance of intraday trading, liquidity risk, optimal order placement as well as high-frequency volatility. This book provides a state-of-the art overview on the major approaches in high-frequency econometrics, including univariate and multivariate autoregressive conditional mean approaches for different types of high-frequency variables, intensity-based approaches for financial point processes and dynamic factor models. It discusses implementation details, provides insights into properties of high-frequency data as well as institutional settings and presents applications to volatility and liquidity estimation, order book modelling and market microstructure analysis.

Download or read book Large Volatility Matrix Inference Based on High frequency Financial Data written by and published by . This book was released on 2013 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt: Financial practices often need to estimate an integrated volatility matrix of a large number of assets using noisy high-frequency financial data. This estimation problem is a challenging one for four reasons: (1) high-frequency financial data are discrete observations of the underlying assets' price processes; (2) due to market micro-structure noise, high-frequency data are observed with measurement errors; (3) different assets are traded at different time points, which is the so-called non-synchronization phenomenon in high-frequency financial data; (4) the number of assets may be comparable to or even exceed the observations, and hence many existing estimators of small size volatility matrices become inconsistent when the size of the matrix is close to or larger than the sample size. In this dissertation, we focus on large volatility matrix inference for high-frequency financial data, which can be summarized in three aspects. On the methodological aspect, we propose a new threshold MSRVM estimator of large volatility matrix. This estimator can deal with all the four challenges, and is consistent when both sample size and matrix size go to infinity. On the theoretical aspect, we study the optimal convergence rate for the volatility matrix estimation, by building the asymptotic theory for the proposed estimator and deriving a minimax lower bound for this estimation problem. The proposed threshold MSRVM estimator has a risk matching with the lower bound up to a constant factor, and hence it achieves an optimal convergence rate. As for the applications, we develop a novel approach to predict the volatility matrix. The approach extends the applicability of classical low-frequency models such as matrix factor models and vector autoregressive models to the high-frequency data. With this approach, we pool together the strengths of both classical low-frequency models and new high-frequency estimation methodologies. Furthermore, numerical studies are conducted to test the finite sample performance of the proposed estimators, to support the established asymptotic theories.

Download or read book Recent Advances in Theory and Methods for the Analysis of High Dimensional and High Frequency Financial Data written by Norman R. Swanson and published by MDPI. This book was released on 2021-08-31 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recently, considerable attention has been placed on the development and application of tools useful for the analysis of the high-dimensional and/or high-frequency datasets that now dominate the landscape. The purpose of this Special Issue is to collect both methodological and empirical papers that develop and utilize state-of-the-art econometric techniques for the analysis of such data.

Download or read book Handbook of High Frequency Trading and Modeling in Finance written by Ionut Florescu and published by John Wiley & Sons. This book was released on 2016-04-05 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt: Reflecting the fast pace and ever-evolving nature of the financial industry, the Handbook of High-Frequency Trading and Modeling in Finance details how high-frequency analysis presents new systematic approaches to implementing quantitative activities with high-frequency financial data. Introducing new and established mathematical foundations necessary to analyze realistic market models and scenarios, the handbook begins with a presentation of the dynamics and complexity of futures and derivatives markets as well as a portfolio optimization problem using quantum computers. Subsequently, the handbook addresses estimating complex model parameters using high-frequency data. Finally, the handbook focuses on the links between models used in financial markets and models used in other research areas such as geophysics, fossil records, and earthquake studies. The Handbook of High-Frequency Trading and Modeling in Finance also features: • Contributions by well-known experts within the academic, industrial, and regulatory fields • A well-structured outline on the various data analysis methodologies used to identify new trading opportunities • Newly emerging quantitative tools that address growing concerns relating to high-frequency data such as stochastic volatility and volatility tracking; stochastic jump processes for limit-order books and broader market indicators; and options markets • Practical applications using real-world data to help readers better understand the presented material The Handbook of High-Frequency Trading and Modeling in Finance is an excellent reference for professionals in the fields of business, applied statistics, econometrics, and financial engineering. The handbook is also a good supplement for graduate and MBA-level courses on quantitative finance, volatility, and financial econometrics. Ionut Florescu, PhD, is Research Associate Professor in Financial Engineering and Director of the Hanlon Financial Systems Laboratory at Stevens Institute of Technology. His research interests include stochastic volatility, stochastic partial differential equations, Monte Carlo Methods, and numerical methods for stochastic processes. Dr. Florescu is the author of Probability and Stochastic Processes, the coauthor of Handbook of Probability, and the coeditor of Handbook of Modeling High-Frequency Data in Finance, all published by Wiley. Maria C. Mariani, PhD, is Shigeko K. Chan Distinguished Professor in Mathematical Sciences and Chair of the Department of Mathematical Sciences at The University of Texas at El Paso. Her research interests include mathematical finance, applied mathematics, geophysics, nonlinear and stochastic partial differential equations and numerical methods. Dr. Mariani is the coeditor of Handbook of Modeling High-Frequency Data in Finance, also published by Wiley. H. Eugene Stanley, PhD, is William Fairfield Warren Distinguished Professor at Boston University. Stanley is one of the key founders of the new interdisciplinary field of econophysics, and has an ISI Hirsch index H=128 based on more than 1200 papers. In 2004 he was elected to the National Academy of Sciences. Frederi G. Viens, PhD, is Professor of Statistics and Mathematics and Director of the Computational Finance Program at Purdue University. He holds more than two dozen local, regional, and national awards and he travels extensively on a world-wide basis to deliver lectures on his research interests, which range from quantitative finance to climate science and agricultural economics. A Fellow of the Institute of Mathematics Statistics, Dr. Viens is the coeditor of Handbook of Modeling High-Frequency Data in Finance, also published by Wiley.

Download or read book Handbook of Financial Time Series written by Torben Gustav Andersen and published by Springer Science & Business Media. This book was released on 2009-04-21 with total page 1045 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Handbook of Financial Time Series gives an up-to-date overview of the field and covers all relevant topics both from a statistical and an econometrical point of view. There are many fine contributions, and a preamble by Nobel Prize winner Robert F. Engle.

Download or read book An Introduction to High Frequency Finance written by Ramazan Gençay and published by Elsevier. This book was released on 2001-05-29 with total page 411 pages. Available in PDF, EPUB and Kindle. Book excerpt: Liquid markets generate hundreds or thousands of ticks (the minimum change in price a security can have, either up or down) every business day. Data vendors such as Reuters transmit more than 275,000 prices per day for foreign exchange spot rates alone. Thus, high-frequency data can be a fundamental object of study, as traders make decisions by observing high-frequency or tick-by-tick data. Yet most studies published in financial literature deal with low frequency, regularly spaced data. For a variety of reasons, high-frequency data are becoming a way for understanding market microstructure. This book discusses the best mathematical models and tools for dealing with such vast amounts of data. This book provides a framework for the analysis, modeling, and inference of high frequency financial time series. With particular emphasis on foreign exchange markets, as well as currency, interest rate, and bond futures markets, this unified view of high frequency time series methods investigates the price formation process and concludes by reviewing techniques for constructing systematic trading models for financial assets.

Download or read book Statistical Inferences on High frequency Financial Data and Quantum State Tomography written by and published by . This book was released on 2016 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this dissertation, we study two topics, the volatility analysis based on the high-frequency financial data and quantum state tomography. 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 Itô 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 Itô 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. 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.

Download or read book Risk Estimation on High Frequency Financial Data written by Florian Jacob and published by Springer. This book was released on 2015-03-28 with total page 78 pages. Available in PDF, EPUB and Kindle. Book excerpt: By studying the ability of the Normal Tempered Stable (NTS) model to fit the statistical features of intraday data at a 5 min sampling frequency, Florian Jacobs extends the research on high frequency data as well as the appliance of tempered stable models. He examines the DAX30 returns using ARMA-GARCH NTS, ARMA-GARCH MNTS (Multivariate Normal Tempered Stable) and ARMA-FIGARCH (Fractionally Integrated GARCH) NTS. The models will be benchmarked through their goodness of fit and their VaR and AVaR, as well as in an historical Backtesting.

Download or read book Inference for Heavy Tailed Data written by Liang Peng and published by Academic Press. This book was released on 2017-08-11 with total page 182 pages. Available in PDF, EPUB and Kindle. Book excerpt: Heavy tailed data appears frequently in social science, internet traffic, insurance and finance. Statistical inference has been studied for many years, which includes recent bias-reduction estimation for tail index and high quantiles with applications in risk management, empirical likelihood based interval estimation for tail index and high quantiles, hypothesis tests for heavy tails, the choice of sample fraction in tail index and high quantile inference. These results for independent data, dependent data, linear time series and nonlinear time series are scattered in different statistics journals. Inference for Heavy-Tailed Data Analysis puts these methods into a single place with a clear picture on learning and using these techniques. Contains comprehensive coverage of new techniques of heavy tailed data analysis Provides examples of heavy tailed data and its uses Brings together, in a single place, a clear picture on learning and using these techniques

Download or read book High frequency data analysis written by Nadine Hirte and published by GRIN Verlag. This book was released on 2004-06-23 with total page 30 pages. Available in PDF, EPUB and Kindle. Book excerpt: Seminar paper from the year 2003 in the subject Mathematics - Statistics, grade: 2.0 (B), European University Viadrina Frankfurt (Oder), language: English, abstract: Today the financial market becomes more complex and includes more competition. Reasons are trends like globalization, liberalization and lower-cost trading mechanism. The market microstructure research has the aim of an efficient market. It is focused on the structure of the financial market. The investigation becomes possible through the availability of high- frequency data. Those data exist especially in the United States and like that most of the research focuses this market. To explain the phenomena, which have been found adequate, models that fit the characteristics of high- frequency data have to be developed. The research is important to understand actions on the market as well as develop new efficient mechanism. One part of the market microstructure field is the bid-ask spread. It will be focus of this paper. In the first two parts it will be discussed theoretically. In the last part one model will be empirically analyzed and tested on its usefulness and validity. The second part of this paper explains the basic elements surrounding the research of bid-ask spread. Those are the financial market, market microstructure as well as high-frequency data. In the following part the bid-ask spread itself, approaches, researches and models focussing the spread will be discussed. The model of Roll (1984) will be explained in detail. The last part will be the empirical analysis of the model of Roll. It is analyzed with data from the NASDAQ.

Download or read book Empirical Properties of Functional Regression Models and Application to High Frequency Financial Data written by Zhang, Xi and published by . This book was released on 2013 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Functional data analysis (FDA) has grown into a substantial field of statistical research, with new methodology, numerous useful applications and interesting novel theoretical developments. My dissertation focuses on the empirical properties of functional regression models and their application to financial data. We start from testing the empirical properties of forecasts with the functional autoregressive models based on simulated and real data. We define intraday returns and consider their prediction from such returns on a market index. This is an extension to intraday data of the Capital Asset Pricing model. Finally we investigate multifactor functional models and assess their suitability for the prediction of intraday returns for various financial assets, including stock and commodity futures.