Download or read book Dynamic Modelling of Large Dimensional Covariance Matrices written by Valeri Voev and published by . This book was released on 2007 with total page 21 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modelling and forecasting the covariance of fiancial return series has always been a challenge due to the so-called curse of dimensionality. This paper proposes a methodology that is applicable in large dimensional cases and is based on a time series of realized covariance matrices. Some solutions are also presented to the problem of non-positive definite forecasts. This methodology is then compared to some traditional models on the basis of its forecasting performance employing Diebold-Mariano tests. We show that our approach is better suited to capture the dynamic features of volatilities and covolatilities compared to the sample covariance based models.

Download or read book Large Dimensional Factor Analysis written by Jushan Bai and published by Now Publishers Inc. This book was released on 2008 with total page 90 pages. Available in PDF, EPUB and Kindle. Book excerpt: Large Dimensional Factor Analysis provides a survey of the main theoretical results for large dimensional factor models, emphasizing results that have implications for empirical work. The authors focus on the development of the static factor models and on the use of estimated factors in subsequent estimation and inference. Large Dimensional Factor Analysis discusses how to determine the number of factors, how to conduct inference when estimated factors are used in regressions, how to assess the adequacy pf observed variables as proxies for latent factors, how to exploit the estimated factors to test unit root tests and common trends, and how to estimate panel cointegration models.

Download or read book Factor State Space Models for High Dimensional Realized Covariance Matrices of Asset Returns written by Bastian Gribisch and published by . This book was released on 2018 with total page 46 pages. Available in PDF, EPUB and Kindle. Book excerpt: We propose a dynamic factor state-space model for high-dimensional covariance matrices of asset returns. It uses observed risk factors and assumes that the latent covariance matrix of assets and factors is observed through their realized covariance matrix with a Wishart measurement density. The imposed strict factor structure allows for dynamics in the covariances of the factors and the residual components as well as in the factor loadings. The model structure facilitates inference using simple Bayesian MCMC procedures making the approach scalable w.r.t. the number of assets. An empirical application shows that the model performs very well in-and-out-of-sample.

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 Large Dynamic Covariance Matrices written by Robert F. Engle 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 A Dynamic Component Model for Forecasting High Dimensional Realized Covariance Matrices written by Luc Bauwens and published by . This book was released on 2017 with total page 24 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Multiplicative MIDAS Realized DCC (MMReDCC) model simultaneously accounts for short and long term dynamics in the conditional (co)volatilities of asset returns, in line with the empirical evidence suggesting that their level is changing over time as a function of economic conditions. Herein the applicability of the model is improved along two directions.First, by proposing an algorithm that relies on the maximization of an iteratively re-computed moment-based profile likelihood function and keeps estimation feasible in large dimensions by mitigating the incidental parameter problem.Second, by illustrating a conditional bootstrap procedure to generate multi-step ahead predictions from the model. In an empirical application on a dataset of forty-six equities, the MMReDCC model is found to statistically outperform the selected benchmarks in terms of in-sample fit as well as in terms of out-of-sample covariance predictions. The latter are mostly significant in periods of high market volatility.

Download or read book Spectral Theory Of Large Dimensional Random Matrices And Its Applications To Wireless Communications And Finance Statistics Random Matrix Theory And Its Applications written by Zhaoben Fang and published by World Scientific. This book was released on 2014-01-24 with total page 233 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book contains three parts: Spectral theory of large dimensional random matrices; Applications to wireless communications; and Applications to finance. In the first part, we introduce some basic theorems of spectral analysis of large dimensional random matrices that are obtained under finite moment conditions, such as the limiting spectral distributions of Wigner matrix and that of large dimensional sample covariance matrix, limits of extreme eigenvalues, and the central limit theorems for linear spectral statistics. In the second part, we introduce some basic examples of applications of random matrix theory to wireless communications and in the third part, we present some examples of Applications to statistical finance.

Download or read book On Market Timing and Investment Performance Part II Statistical Procedures for Evaluating Forecasting Skills written by Roy Henriksson and published by . This book was released on 2023-07-18 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Reparametrized Dynamic Space Time Models and Spatial Model Selection written by and published by . This book was released on 2004 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Researchers in diverse areas such as environmental and health sciences are increasingly facing working with space-time data. Often the dimension of space-time data sets can be very large and moreover, space-time processes are often complicated in that the dependence structure across space and time is non-trivial, often non-separable and non-stationary in space and/or time. Hence, space-time modeling is a challenging task and in particular parameter estimation can be problematic due to the high dimensionality. We propose a reparametrization approach to fit dynamic space-time models with an unstructured covariance function. Our modeling contribution is to present unconstrained reparametrization for a covariance matrix in dynamic space-time models. Using this unconstrained reparametrization method, we are able to implement the modeling of a high dimensional covariance matrix that automatically maintains the positive definiteness constraint. We illustrate the use of this reparametrization method by applying our model to a set of atmospheric nitrate concentration data. We also consider the problem of model selection for spatial data. The issue of model selection in spatial models has rarely been addressed in the literature, though it is very important. To address this problem, we consider selection criteria such as the Akaike Information Criterion (AIC), Corrected Akaike Information Criterion (AICc) and Bayesian Information Criterion (BIC). The performance of these selection criteria are examined using Monte Carlo simulations. In particular, the ability of these criteria to select the correct model is evaluated.

Download or read book High Frequency Financial Econometrics written by Luc Bauwens and published by Springer Science & Business Media. This book was released on 2007-12-31 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: Shedding light on some of the most pressing open questions in the analysis of high frequency data, this volume presents cutting-edge developments in high frequency financial econometrics. Coverage spans a diverse range of topics, including market microstructure, tick-by-tick data, bond and foreign exchange markets, and large dimensional volatility modeling. The volume is of interest to graduate students, researchers, and industry professionals.

Download or read book Structural Dynamics Volume 3 written by Tom Proulx and published by Springer Science & Business Media. This book was released on 2011-06-10 with total page 1545 pages. Available in PDF, EPUB and Kindle. Book excerpt: This the fifth volume of five from the 28th IMAC on Structural Dynamics and Renewable Energy, 2010,, brings together 146 chapters on Structural Dynamics. It presents early findings from experimental and computational investigations of on a wide range of area within Structural Dynamics, including studies such as Simulation and Validation of ODS Measurements made Using a Continuous SLDV Method on a Beam Excited by a Pseudo Random Signal, Comparison of Image Based, Laser, and Accelerometer Measurements, Modal Parameter Estimation Using Acoustic Modal Analysis, Mitigation of Vortex-induced Vibrations in Long-span Bridges, and Vibration and Acoustic Analysis of Brake Pads for Quality Control.

Download or read book A New Semiparametric Estimation Approach for Large Dynamic Covariance Matrices with Multiple Conditioning Variables written by Jia Chen and published by . This book was released on 2018 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Large Covariance and Autocovariance Matrices written by Arup Bose and published by CRC Press. This book was released on 2018-07-03 with total page 359 pages. Available in PDF, EPUB and Kindle. Book excerpt: Large Covariance and Autocovariance Matrices brings together a collection of recent results on sample covariance and autocovariance matrices in high-dimensional models and novel ideas on how to use them for statistical inference in one or more high-dimensional time series models. The prerequisites include knowledge of elementary multivariate analysis, basic time series analysis and basic results in stochastic convergence. Part I is on different methods of estimation of large covariance matrices and auto-covariance matrices and properties of these estimators. Part II covers the relevant material on random matrix theory and non-commutative probability. Part III provides results on limit spectra and asymptotic normality of traces of symmetric matrix polynomial functions of sample auto-covariance matrices in high-dimensional linear time series models. These are used to develop graphical and significance tests for different hypotheses involving one or more independent high-dimensional linear time series. The book should be of interest to people in econometrics and statistics (large covariance matrices and high-dimensional time series), mathematics (random matrices and free probability) and computer science (wireless communication). Parts of it can be used in post-graduate courses on high-dimensional statistical inference, high-dimensional random matrices and high-dimensional time series models. It should be particularly attractive to researchers developing statistical methods in high-dimensional time series models. Arup Bose is a professor at the Indian Statistical Institute, Kolkata, India. He is a distinguished researcher in mathematical statistics and has been working in high-dimensional random matrices for the last fifteen years. He has been editor of Sankhyā for several years and has been on the editorial board of several other journals. He is a Fellow of the Institute of Mathematical Statistics, USA and all three national science academies of India, as well as the recipient of the S.S. Bhatnagar Award and the C.R. Rao Award. His first book Patterned Random Matrices was also published by Chapman & Hall. He has a forthcoming graduate text U-statistics, M-estimates and Resampling (with Snigdhansu Chatterjee) to be published by Hindustan Book Agency. Monika Bhattacharjee is a post-doctoral fellow at the Informatics Institute, University of Florida. After graduating from St. Xavier's College, Kolkata, she obtained her master’s in 2012 and PhD in 2016 from the Indian Statistical Institute. Her thesis in high-dimensional covariance and auto-covariance matrices, written under the supervision of Dr. Bose, has received high acclaim.

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 Forecasting a Large Dimensional Covariance Matrix of a Portfolio of Different Asset Classes written by Lillie Lam and published by . This book was released on 2009 with total page 32 pages. Available in PDF, EPUB and Kindle. Book excerpt: In portfolio and risk management, estimating and forecasting the volatilities and correlations of asset returns plays an important role. Recently, interest in the estimation of the covariance matrix of large dimensional portfolios has increased. Using a portfolio of 63 assets covering stocks, bonds and currencies, this paper aims to examine and compare the predictive power of different popular methods adopted by i) market practitioners (such as the sample covariance, the 250-day moving average, and the exponentially weighted moving average); ii) some sophisticated estimators recently developed in the academic literature (such as the orthogonal GARCH model and the Dynamic Conditional Correlation model); and iii) their combinations. Based on five different criteria, we show that a combined forecast of the 250-day moving average, the exponentially weighted moving average and the orthogonal GARCH model consistently outperforms the other methods in predicting the covariance matrix for both one-quarter and one-year ahead horizons.

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 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.