Download or read book Principal Component Analysis of High Frequency Data written by Yacine Ait-Sahalia and published by . This book was released on 2017 with total page 64 pages. Available in PDF, EPUB and Kindle. Book excerpt: We develop the necessary methodology to conduct principal component analysis at high frequency. We construct estimators of realized eigenvalues, eigenvectors, and principal components and provide the asymptotic distribution of these estimators. Empirically, we study the high frequency covariance structure of the constituents of the S&P 100 Index using as little as one week of high frequency data at a time. The explanatory power of the high frequency principal components varies over time. During the recent financial crisis, the first principal component becomes increasingly dominant, explaining up to 60% of the variation on its own, while the second principal component drives the common variation of financial sector stocks.

Download or read book Principal Component Analysis of High Frequency Data written by Yacine Aït-Sahalia and published by . This book was released on 2015 with total page 51 pages. Available in PDF, EPUB and Kindle. Book excerpt: We develop the necessary methodology to conduct principal component analysis at high frequency. We construct estimators of realized eigenvalues, eigenvectors, and principal components and provide the asymptotic distribution of these estimators. Empirically, we study the high frequency covariance structure of the constituents of the S&P 100 Index using as little as one week of high frequency data at a time. The explanatory power of the high frequency principal components varies over time. During the recent financial crisis, the first principal component becomes increasingly dominant, explaining up to 60% of the variation on its own, while the second principal component drives the common variation of financial sector stocks.

Download or read book Principal Component Analysis and Realized Regression with Asynchronous and Noisy High Frequency Data written by Dachuan Chen and published by . This book was released on 2019 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Econometric Forecasting and High frequency Data Analysis written by Roberto S. Mariano and published by World Scientific. This book was released on 2008 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: This important book consists of surveys of high-frequency financial data analysis and econometric forecasting, written by pioneers in these areas including Nobel laureate Lawrence Klein. Some of the chapters were presented as tutorials to an audience in the Econometric Forecasting and High-Frequency Data Analysis Workshop at the Institute for Mathematical Science, National University of Singapore in May 2006. They will be of interest to researchers working in macroeconometrics as well as financial econometrics. Moreover, readers will find these chapters useful as a guide to the literature as well as suggestions for future research. Sample Chapter(s). Foreword (32 KB). Chapter 1: Forecast Uncertainty, Its Representation and Evaluation* (97 KB). Contents: Forecasting Uncertainty, Its Representation and Evaluation (K F Wallis); The University of Pennsylvania Models for High-Frequency Macroeconomic Modeling (L R Klein & S Ozmucur); Forecasting Seasonal Time Series (P H Franses); Car and Affine Processes (C Gourieroux); Multivariate Time Series Analysis and Forecasting (M Deistler). Readership: Professionals and researchers in econometric forecasting and financial data analysis.

Download or read book Principal Component Analysis and Randomness Test for Big Data Analysis written by Mieko Tanaka-Yamawaki and published by Springer Nature. This book was released on 2023-05-23 with total page 153 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the novel approach of analyzing large-sized rectangular-shaped numerical data (so-called big data). The essence of this approach is to grasp the "meaning" of the data instantly, without getting into the details of individual data. Unlike conventional approaches of principal component analysis, randomness tests, and visualization methods, the authors' approach has the benefits of universality and simplicity of data analysis, regardless of data types, structures, or specific field of science. First, mathematical preparation is described. The RMT-PCA and the RMT-test utilize the cross-correlation matrix of time series, C = XXT, where X represents a rectangular matrix of N rows and L columns and XT represents the transverse matrix of X. Because C is symmetric, namely, C = CT, it can be converted to a diagonal matrix of eigenvalues by a similarity transformation SCS-1 = SCST using an orthogonal matrix S. When N is significantly large, the histogram of the eigenvalue distribution can be compared to the theoretical formula derived in the context of the random matrix theory (RMT, in abbreviation). Then the RMT-PCA applied to high-frequency stock prices in Japanese and American markets is dealt with. This approach proves its effectiveness in extracting "trendy" business sectors of the financial market over the prescribed time scale. In this case, X consists of N stock- prices of length L, and the correlation matrix C is an N by N square matrix, whose element at the i-th row and j-th column is the inner product of the price time series of the length L of the i-th stock and the j-th stock of the equal length L. Next, the RMT-test is applied to measure randomness of various random number generators, including algorithmically generated random numbers and physically generated random numbers. The book concludes by demonstrating two applications of the RMT-test: (1) a comparison of hash functions, and (2) stock prediction by means of randomness, including a new index of off-randomness related to market decline.

Download or read book Generalized Principal Component Analysis written by René Vidal and published by Springer. This book was released on 2016-04-11 with total page 590 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a comprehensive introduction to the latest advances in the mathematical theory and computational tools for modeling high-dimensional data drawn from one or multiple low-dimensional subspaces (or manifolds) and potentially corrupted by noise, gross errors, or outliers. This challenging task requires the development of new algebraic, geometric, statistical, and computational methods for efficient and robust estimation and segmentation of one or multiple subspaces. The book also presents interesting real-world applications of these new methods in image processing, image and video segmentation, face recognition and clustering, and hybrid system identification etc. This book is intended to serve as a textbook for graduate students and beginning researchers in data science, machine learning, computer vision, image and signal processing, and systems theory. It contains ample illustrations, examples, and exercises and is made largely self-contained with three Appendices which survey basic concepts and principles from statistics, optimization, and algebraic-geometry used in this book. René Vidal is a Professor of Biomedical Engineering and Director of the Vision Dynamics and Learning Lab at The Johns Hopkins University. Yi Ma is Executive Dean and Professor at the School of Information Science and Technology at ShanghaiTech University. S. Shankar Sastry is Dean of the College of Engineering, Professor of Electrical Engineering and Computer Science and Professor of Bioengineering at the University of California, Berkeley.

Download or read book New Developments in Classification and Data Analysis written by Maurizio Vichi and published by Springer Science & Business Media. This book was released on 2006-05-06 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains revised versions of selected papers presented during the biannual meeting of the Classification and Data Analysis Group of SocietA Italiana di Statistica, which was held in Bologna, September 22-24, 2003. The scientific program of the conference included 80 contributed papers. Moreover it was possible to recruit six internationally renowned invited spe- ers for plenary talks on their current research works regarding the core topics of IFCS (the International Federation of Classification Societies) and Wo- gang Gaul and the colleagues of the GfKl organized a session. Thus, the conference provided a large number of scientists and experts from home and abroad with an attractive forum for discussions and mutual exchange of knowledge. The talks in the different sessions focused on methodological developments in supervised and unsupervised classification and in data analysis, also p- viding relevant contributions in the context of applications. This suggested the presentation of the 43 selected papers in three parts as follows: CLASSIFICATION AND CLUSTERING Non parametric classification Clustering and dissimilarities MULTIVARIATE STATISTICS AND DATA ANALYSIS APPLIED MULTIVARIATE STATISTICS Environmental data Microarray data Behavioural and text data Financial data We wish to express our gratitude to the authors whose enthusiastic p- ticipation made the meeting possible. We are very grateful to the reviewers for the time spent in their professional reviewing work. We would also like to extend our thanks to the chairpersons and discussants of the sessions: their comments and suggestions proved very stimulating both for the authors and the audience.

Download or read book Principal Component Analysis written by I.T. Jolliffe and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 283 pages. Available in PDF, EPUB and Kindle. Book excerpt: Principal component analysis is probably the oldest and best known of the It was first introduced by Pearson (1901), techniques ofmultivariate analysis. and developed independently by Hotelling (1933). Like many multivariate methods, it was not widely used until the advent of electronic computers, but it is now weIl entrenched in virtually every statistical computer package. The central idea of principal component analysis is to reduce the dimen sionality of a data set in which there are a large number of interrelated variables, while retaining as much as possible of the variation present in the data set. This reduction is achieved by transforming to a new set of variables, the principal components, which are uncorrelated, and which are ordered so that the first few retain most of the variation present in all of the original variables. Computation of the principal components reduces to the solution of an eigenvalue-eigenvector problem for a positive-semidefinite symmetrie matrix. Thus, the definition and computation of principal components are straightforward but, as will be seen, this apparently simple technique has a wide variety of different applications, as weIl as a number of different deri vations. Any feelings that principal component analysis is a narrow subject should soon be dispelled by the present book; indeed some quite broad topics which are related to principal component analysis receive no more than a brief mention in the final two chapters.

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 Multivariate Time Series Analysis and Applications written by William W. S. Wei and published by John Wiley & Sons. This book was released on 2019-03-18 with total page 536 pages. Available in PDF, EPUB and Kindle. Book excerpt: An essential guide on high dimensional multivariate time series including all the latest topics from one of the leading experts in the field Following the highly successful and much lauded book, Time Series Analysis—Univariate and Multivariate Methods, this new work by William W.S. Wei focuses on high dimensional multivariate time series, and is illustrated with numerous high dimensional empirical time series. Beginning with the fundamentalconcepts and issues of multivariate time series analysis,this book covers many topics that are not found in general multivariate time series books. Some of these are repeated measurements, space-time series modelling, and dimension reduction. The book also looks at vector time series models, multivariate time series regression models, and principle component analysis of multivariate time series. Additionally, it provides readers with information on factor analysis of multivariate time series, multivariate GARCH models, and multivariate spectral analysis of time series. With the development of computers and the internet, we have increased potential for data exploration. In the next few years, dimension will become a more serious problem. Multivariate Time Series Analysis and its Applications provides some initial solutions, which may encourage the development of related software needed for the high dimensional multivariate time series analysis. Written by bestselling author and leading expert in the field Covers topics not yet explored in current multivariate books Features classroom tested material Written specifically for time series courses Multivariate Time Series Analysis and its Applications is designed for an advanced time series analysis course. It is a must-have for anyone studying time series analysis and is also relevant for students in economics, biostatistics, and engineering.

Download or read book Using Principal Component Analysis to Estimate a Highdimensional Factor Model with High frequency Data written by Yacine Aït-Sahalia and published by . This book was released on 2017 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book The Five Trolls Under the Bridge written by Dachuan Chen and published by . This book was released on 2018 with total page 78 pages. Available in PDF, EPUB and Kindle. Book excerpt: We develop a principal component analysis (PCA) for high frequency data. As in Northern fairly tales, there are trolls waiting for the explorer. The first three trolls are market microstructure noise, asynchronous sampling times, and edge effects in estimators. To get around these, a robust estimator of spot covariance matrix is developed based on the Smoothed TSRV (Mykland et al. (2017)). The fourth troll is how to pass from estimated time-varying covariance matrix to PCA. Under finite dimensionality, we develop this methodology through the estimation of realized spectral functions. Rates of convergence and central limit theory, as well as an estimator of standard error, are established. The fifth troll is high dimension on top of high frequency, where we also develop PCA. With the help of a new identity concerning the spot principal orthogonal complement, the high-dimensional rates of convergence have been studied by freeing several strong assumptions in classical PCA. As an application, we show that our first principal component (PC) potentially outperforms the S&P 100 market index, while three of the next four PCs are cointegrated with two of the Fama-French non-market factors.

Download or read book Topics in Random Matrix Theory written by Terence Tao and published by American Mathematical Soc.. This book was released on 2012-03-21 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: The field of random matrix theory has seen an explosion of activity in recent years, with connections to many areas of mathematics and physics. However, this makes the current state of the field almost too large to survey in a single book. In this graduate text, we focus on one specific sector of the field, namely the spectral distribution of random Wigner matrix ensembles (such as the Gaussian Unitary Ensemble), as well as iid matrix ensembles. The text is largely self-contained and starts with a review of relevant aspects of probability theory and linear algebra. With over 200 exercises, the book is suitable as an introductory text for beginning graduate students seeking to enter the field.

Download or read book Discretization of Processes written by Jean Jacod and published by Springer Science & Business Media. This book was released on 2011-10-22 with total page 596 pages. Available in PDF, EPUB and Kindle. Book excerpt: In applications, and especially in mathematical finance, random time-dependent events are often modeled as stochastic processes. Assumptions are made about the structure of such processes, and serious researchers will want to justify those assumptions through the use of data. As statisticians are wont to say, “In God we trust; all others must bring data.” This book establishes the theory of how to go about estimating not just scalar parameters about a proposed model, but also the underlying structure of the model itself. Classic statistical tools are used: the law of large numbers, and the central limit theorem. Researchers have recently developed creative and original methods to use these tools in sophisticated (but highly technical) ways to reveal new details about the underlying structure. For the first time in book form, the authors present these latest techniques, based on research from the last 10 years. They include new findings. This book will be of special interest to researchers, combining the theory of mathematical finance with its investigation using market data, and it will also prove to be useful in a broad range of applications, such as to mathematical biology, chemical engineering, and physics.

Download or read book Advances in Longitudinal Data Methods in Applied Economic Research written by Nicholas Tsounis and published by Springer Nature. This book was released on 2021-03-31 with total page 545 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents new methods and applications in longitudinal data estimation methodology in applied economic. Featuring selected papers from the 2020 the International Conference on Applied Economics (ICOAE 2020) held virtually due to the corona virus pandemic, this book examines interdisciplinary topics such as financial economics, international economics, agricultural economics, marketing and management. Country specific case studies are also featured.

Download or read book A Dynamic Use Of Survey Data And High Frequency Model Forecasting written by Yoshihisa Inada and published by World Scientific. This book was released on 2018-03-08 with total page 126 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume investigates the accuracy and dynamic performance of a high-frequency forecast model for the Japanese and United States economies based on the Current Quarter Model (CQM) or High Frequency Model (HFM) developed by the late Professor Emeritus Lawrence R. Klein. It also presents a survey of recent developments in high-frequency forecasts and gives an example application of the CQM model in forecasting Gross Regional Products (GRPs).

Download or read book Principal Component Analysis written by Parinya Sanguansat and published by BoD – Books on Demand. This book was released on 2012-03-07 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is aimed at raising awareness of researchers, scientists and engineers on the benefits of Principal Component Analysis (PCA) in data analysis. In this book, the reader will find the applications of PCA in fields such as energy, multi-sensor data fusion, materials science, gas chromatographic analysis, ecology, video and image processing, agriculture, color coating, climate and automatic target recognition.