Download or read book Three Essays on Covariance Matrix Estimation and Factor Models in High Dimensions written by Aygul Zagidullina and published by . This book was released on 2019 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Essays on Applications of the Factor Model written by Xiaolin Sun and published by . This book was released on 2013 with total page 61 pages. Available in PDF, EPUB and Kindle. Book excerpt: Estimating the volatilities and correlations of asset returns plays an important role in portfolio and risk management. As of late, interest in the estimation of the covariance matrix of large dimensional portfolios has increased. Estimating large dimensional covariance poses a challenge in that the cross-sectional dimension is often similar to or bigger than the number of observations available. Simple estimators are often poorly conditioned with some small eigenvalues, and so are unsuitable for many real world applications, including portfolio optimization and tracking error minimization. The first chapter introduces our two large dimensional covariance matrix estimators. We estimate the large dimensional realized covariance matrix by using the methods of asymptotic principal components analysis based factor modeling and singular value decomposition. In the second chapter, we show though simulation that our proposed estimators are closer to the true covariance matrix than the current popular shrinkage estimator. We also simulate conducting the out sample portfolio performance tests and find that the portfolios constructed based on our proposed estimators have lower risk than portfolios constructed using the shrinkage matrix. Using S&P 500 stocks from 1926 to 2011, we back test our proposed covariance matrix. In addition, the portfolios constructed based on our proposed estimators exhibit lower risk than portfolios constructed using the shrinkage matrix. The third chapter proposes a new volatility index--a cross-sectional volatility index of residuals using factor model. The cross-sectional volatility index moves closely with the VIX for the S&P 500 stock universe. It is a non-parametric, model-free volatility index, which could be estimated at any frequency for any region, sector, and style of world equity market and also does not depend on any option pricing. We provide some interpretation of the cross-sectional volatility index of residuals as a proxy for aggregate economic uncertainty, and show a high correlation between the VIX index and the corresponding cross-sectional volatility index of residuals based on the S&P 500 universe. Our results show that the portfolio hedged based on the cross-sectional volatility index of residuals has a much higher Sharpe ratio than the portfolio without hedge. Overall, these findings suggest that the cross-sectional volatility index of residuals is intimately related to other volatility measures where and when such measures are available, and that it can be used as a reliable proxy for volatility when such measures are not available.

Download or read book High Dimensional Covariance Estimation written by Mohsen Pourahmadi and published by John Wiley & Sons. This book was released on 2013-06-24 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: Methods for estimating sparse and large covariance matrices Covariance and correlation matrices play fundamental roles in every aspect of the analysis of multivariate data collected from a variety of fields including business and economics, health care, engineering, and environmental and physical sciences. High-Dimensional Covariance Estimation provides accessible and comprehensive coverage of the classical and modern approaches for estimating covariance matrices as well as their applications to the rapidly developing areas lying at the intersection of statistics and machine learning. Recently, the classical sample covariance methodologies have been modified and improved upon to meet the needs of statisticians and researchers dealing with large correlated datasets. High-Dimensional Covariance Estimation focuses on the methodologies based on shrinkage, thresholding, and penalized likelihood with applications to Gaussian graphical models, prediction, and mean-variance portfolio management. The book relies heavily on regression-based ideas and interpretations to connect and unify many existing methods and algorithms for the task. High-Dimensional Covariance Estimation features chapters on: Data, Sparsity, and Regularization Regularizing the Eigenstructure Banding, Tapering, and Thresholding Covariance Matrices Sparse Gaussian Graphical Models Multivariate Regression The book is an ideal resource for researchers in statistics, mathematics, business and economics, computer sciences, and engineering, as well as a useful text or supplement for graduate-level courses in multivariate analysis, covariance estimation, statistical learning, and high-dimensional data analysis.

Download or read book Error Covariance Matrix Estimation in High Dimensional Approximate Factor Models Using Adaptive Thresholding written by Paul J. Chimenti and published by . This book was released on 2013 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: Approximate factor models are popular in nance and economics. A key to eectively utilizing such a model is to accurately estimate the error covariance matrix. Errors related to certain predictors are expected to be correlated and this must be modeled eectively. Adaptive thresholding is a method for estimating the error covariance matrix of such a model. This method is described in detail and a simulation study sheds light on the behavior of this method under dierent sample sizes and parameterizations.

Download or read book Essays in Honor of Cheng Hsiao written by Dek Terrell and published by Emerald Group Publishing. This book was released on 2020-04-15 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: Including contributions spanning a variety of theoretical and applied topics in econometrics, this volume of Advances in Econometrics is published in honour of Cheng Hsiao.

Download or read book Large Dimensional Covariance Matrix Estimation Via a Factor Model written by Jianqing Fan and published by . This book was released on 2007 with total page 55 pages. Available in PDF, EPUB and Kindle. Book excerpt: High dimensionality comparable to sample size is common in many statistical problems. We examine covariance matrix estimation in the asymptotic framework that the dimensionality p tends to infinity as the sample size n increases. Motivated by the Arbitrage Pricing Theory in finance, a multi-factor model is employed to reduce dimensionality and to estimate the covariance matrix. The factors are observable and the number of factors K is allowed to grow with p. We investigate impact of p and K on the performance of the model-based covariance matrix estimator. Under mild assumptions, we have established convergence rates and asymptotic normality of the model-based estimator. Its performance is compared with that of the sample covariance matrix. We identify situations under which the factor approach increases performance substantially or marginally. The impacts of covariance matrix estimation on portfolio allocation and risk management are studied. The asymptotic results are supported by a thorough simulation study.

Download or read book Selected Works of Peter J Bickel written by Jianqing Fan and published by Springer Science & Business Media. This book was released on 2012-11-28 with total page 626 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents selections of Peter J. Bickel’s major papers, along with comments on their novelty and impact on the subsequent development of statistics as a discipline. Each of the eight parts concerns a particular area of research and provides new commentary by experts in the area. The parts range from Rank-Based Nonparametrics to Function Estimation and Bootstrap Resampling. Peter’s amazing career encompasses the majority of statistical developments in the last half-century or about about half of the entire history of the systematic development of statistics. This volume shares insights on these exciting statistical developments with future generations of statisticians. The compilation of supporting material about Peter’s life and work help readers understand the environment under which his research was conducted. The material will also inspire readers in their own research-based pursuits. This volume includes new photos of Peter Bickel, his biography, publication list, and a list of his students. These give the reader a more complete picture of Peter Bickel as a teacher, a friend, a colleague, and a family man.

Download or read book High Dimensional Covariance Matrix Estimation Shrinkage Toward a Diagonal Target written by Mr. Sakai Ando and published by International Monetary Fund. This book was released on 2023-12-08 with total page 32 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper proposes a novel shrinkage estimator for high-dimensional covariance matrices by extending the Oracle Approximating Shrinkage (OAS) of Chen et al. (2009) to target the diagonal elements of the sample covariance matrix. We derive the closed-form solution of the shrinkage parameter and show by simulation that, when the diagonal elements of the true covariance matrix exhibit substantial variation, our method reduces the Mean Squared Error, compared with the OAS that targets an average variance. The improvement is larger when the true covariance matrix is sparser. Our method also reduces the Mean Squared Error for the inverse of the covariance matrix.

Download or read book Data Mining for Bioinformatics written by Sumeet Dua and published by CRC Press. This book was released on 2012-11-06 with total page 351 pages. Available in PDF, EPUB and Kindle. Book excerpt: Covering theory, algorithms, and methodologies, as well as data mining technologies, Data Mining for Bioinformatics provides a comprehensive discussion of data-intensive computations used in data mining with applications in bioinformatics. It supplies a broad, yet in-depth, overview of the application domains of data mining for bioinformatics to help readers from both biology and computer science backgrounds gain an enhanced understanding of this cross-disciplinary field. The book offers authoritative coverage of data mining techniques, technologies, and frameworks used for storing, analyzing, and extracting knowledge from large databases in the bioinformatics domains, including genomics and proteomics. It begins by describing the evolution of bioinformatics and highlighting the challenges that can be addressed using data mining techniques. Introducing the various data mining techniques that can be employed in biological databases, the text is organized into four sections: Supplies a complete overview of the evolution of the field and its intersection with computational learning Describes the role of data mining in analyzing large biological databases—explaining the breath of the various feature selection and feature extraction techniques that data mining has to offer Focuses on concepts of unsupervised learning using clustering techniques and its application to large biological data Covers supervised learning using classification techniques most commonly used in bioinformatics—addressing the need for validation and benchmarking of inferences derived using either clustering or classification The book describes the various biological databases prominently referred to in bioinformatics and includes a detailed list of the applications of advanced clustering algorithms used in bioinformatics. Highlighting the challenges encountered during the application of classification on biological databases, it considers systems of both single and ensemble classifiers and shares effort-saving tips for model selection and performance estimation strategies.

Download or read book Pivotal Variable Detection of the Covariance Matrix and Its Application to High Dimensional Factor Models written by Junlong Zhao and published by . This book was released on 2017 with total page 44 pages. Available in PDF, EPUB and Kindle. Book excerpt: To estimate the high-dimensional covariance matrix, row sparsity is often assumed such that each row has a small number of nonzero elements. However, in some applications, such as factor modeling, there may be many non-zero loadings of the common factors. The corresponding variables are also correlated to one another and the rows are non-sparse or dense. This paper has three main aims. First,a detection method is proposed to identify the rows that may be non-sparse, or at least dense with many non-zero elements. These rows are called dense rows and the corresponding variables are called pivotal variables. Second, to determine the number of rows, a ridge ratio method is suggested, which can be regarded as a sure screening procedure. Third, to handle the estimation of high-dimensional factor models, a two-step procedure is suggested with the above screening as the first step. Simulations are conducted to examine the performance.

Download or read book Handbook of Volatility Models and Their Applications written by Luc Bauwens and published by John Wiley & Sons. This book was released on 2012-04-17 with total page 566 pages. Available in PDF, EPUB and Kindle. Book excerpt: A complete guide to the theory and practice of volatility models in financial engineering Volatility has become a hot topic in this era of instant communications, spawning a great deal of research in empirical finance and time series econometrics. Providing an overview of the most recent advances, Handbook of Volatility Models and Their Applications explores key concepts and topics essential for modeling the volatility of financial time series, both univariate and multivariate, parametric and non-parametric, high-frequency and low-frequency. Featuring contributions from international experts in the field, the book features numerous examples and applications from real-world projects and cutting-edge research, showing step by step how to use various methods accurately and efficiently when assessing volatility rates. Following a comprehensive introduction to the topic, readers are provided with three distinct sections that unify the statistical and practical aspects of volatility: Autoregressive Conditional Heteroskedasticity and Stochastic Volatility presents ARCH and stochastic volatility models, with a focus on recent research topics including mean, volatility, and skewness spillovers in equity markets Other Models and Methods presents alternative approaches, such as multiplicative error models, nonparametric and semi-parametric models, and copula-based models of (co)volatilities Realized Volatility explores issues of the measurement of volatility by realized variances and covariances, guiding readers on how to successfully model and forecast these measures Handbook of Volatility Models and Their Applications is an essential reference for academics and practitioners in finance, business, and econometrics who work with volatility models in their everyday work. The book also serves as a supplement for courses on risk management and volatility at the upper-undergraduate and graduate levels.

Download or read book Essays in Nonlinear Time Series Econometrics written by Niels Haldrup and published by OUP Oxford. This book was released on 2014-06-26 with total page 393 pages. Available in PDF, EPUB and Kindle. Book excerpt: This edited collection concerns nonlinear economic relations that involve time. It is divided into four broad themes that all reflect the work and methodology of Professor Timo Teräsvirta, one of the leading scholars in the field of nonlinear time series econometrics. The themes are: Testing for linearity and functional form, specification testing and estimation of nonlinear time series models in the form of smooth transition models, model selection and econometric methodology, and finally applications within the area of financial econometrics. All these research fields include contributions that represent state of the art in econometrics such as testing for neglected nonlinearity in neural network models, time-varying GARCH and smooth transition models, STAR models and common factors in volatility modeling, semi-automatic general to specific model selection for nonlinear dynamic models, high-dimensional data analysis for parametric and semi-parametric regression models with dependent data, commodity price modeling, financial analysts earnings forecasts based on asymmetric loss function, local Gaussian correlation and dependence for asymmetric return dependence, and the use of bootstrap aggregation to improve forecast accuracy. Each chapter represents original scholarly work, and reflects the intellectual impact that Timo Teräsvirta has had and will continue to have, on the profession.

Download or read book Essays in Honour of Fabio Canova written by Juan J. Dolado and published by Emerald Group Publishing. This book was released on 2022-09-21 with total page 203 pages. Available in PDF, EPUB and Kindle. Book excerpt: Both parts of Volume 44 of Advances in Econometrics pay tribute to Fabio Canova for his major contributions to economics over the last four decades.

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 High Dimensional Probability written by Roman Vershynin and published by Cambridge University Press. This book was released on 2018-09-27 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: An integrated package of powerful probabilistic tools and key applications in modern mathematical data science.

Download or read book Time Series in High Dimension the General Dynamic Factor Model written by Marc Hallin and published by World Scientific Publishing Company. This book was released on 2020-03-30 with total page 764 pages. Available in PDF, EPUB and Kindle. Book excerpt: Factor models have become the most successful tool in the analysis and forecasting of high-dimensional time series. This monograph provides an extensive account of the so-called General Dynamic Factor Model methods. The topics covered include: asymptotic representation problems, estimation, forecasting, identification of the number of factors, identification of structural shocks, volatility analysis, and applications to macroeconomic and financial data.

Download or read book Large Dimensional Covariance Matrix Estimation with Decomposition based Regularization written by and published by . This book was released on 2014 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Estimation of population covariance matrices from samples of multivariate data is of great importance. When the dimension of a covariance matrix is large but the sample size is limited, it is well known that the sample covariance matrix is dissatisfactory. However, the improvement of covariance matrix estimation is not straightforward, mainly because of the constraint of positive definiteness. This thesis work considers decomposition-based methods to circumvent this primary difficulty. Two ways of covariance matrix estimation with regularization on factor matrices from decompositions are included. One approach replies on the modified Cholesky decomposition from Pourahmadi, and the other technique, matrix exponential or matrix logarithm, is closely related to the spectral decomposition. We explore the usage of covariance matrix estimation by imposing L1 regularization on the entries of Cholesky factor matrices, and find the estimates from this approach are not sensitive to the orders of variables. A given order of variables is the prerequisite in the application of the modified Cholesky decomposition, while in practice, information on the order of variables is often unknown. We take advantage of this property to remove the requirement of order information, and propose an order-invariant covariance matrix estimate by refining estimates corresponding to different orders of variables. The refinement not only guarantees the positive definiteness of the estimated covariance matrix, but also is applicable in general situations without the order of variables being pre-specified. The refined estimate can be approximated by only combining a moderate number of representative estimates. Numerical simulations are conducted to evaluate the performance of the proposed method in comparison with several other estimates. By applying the matrix exponential technique, the problem of estimating positive definite covariance matrices is transformed into a problem of estimating symmetric matrices. There are close connections between covariance matrices and their logarithm matrices, and thus, pursing a matrix logarithm with certain properties helps restoring the original covariance matrix. The covariance matrix estimate from applying L1 regularization to the entries of the matrix logarithm is compared to some other estimates in simulation studies and real data analysis.