Download or read book Factor GARCH ITO Models for High Frequency Data with Application to Large Volatility Matrix Prediction written by Donggyu Kim and published by . This book was released on 2017 with total page 41 pages. Available in PDF, EPUB and Kindle. Book excerpt: Several novel large volatility matrix estimation methods have been developed based on the high-frequency financial data. They often employ the approximate factor model that leads to a low-rank plus sparse structure for the integrated volatility matrix and facilitates estimation of large volatility matrices. However, for predicting future volatility matrices, these nonparametric estimators do not have a dynamic structure to implement. In this paper, we introduce a novel Ito diffusion process based on the approximate factor models and call it a factor GARCH-Ito model. We then investigate its properties and propose a quasi-maximum likelihood estimation method for the parameter of the factor GARCH-Ito model. We also apply it to estimating conditional expected large volatility matrices and establish their asymptotic properties. Simulation studies are conducted to validate the finite sample performance of the proposed estimation methods. The proposed method is also illustrated by using data from the constituents of the S&P 500 index and an application to constructing the minimum variance portfolio with gross exposure constraints.

Download or read book Factor Overnight GARCH It Models written by Donggyu Kim and published by . This book was released on 2023 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper introduces a unified factor overnight GARCH-Itô Models model for large volatility matrix estimation and prediction. To account for whole-day market dynamics, the proposed model has two different instantaneous factor volatility processes for the open-to-close and close-to-open periods, while each embeds the discrete-time multivariate GARCH model structure. To estimate latent factor volatility, we assume the low rank plus sparse structure and employ non-parametric estimation procedures.Then, based on the connection between the discrete-time model structure and the continuous-time diffusion process, we propose a weighted least squares estimation procedure with the non-parametric factor volatility estimator and establish its asymptotic theorems.

Download or read book Robust High Dimensional Volatility Matrix Estimation for High Frequency Factor Model written by Jianqing Fan and published by . This book was released on 2017 with total page 42 pages. Available in PDF, EPUB and Kindle. Book excerpt: High-frequency financial data allow us to estimate large volatility matrices with relatively short time horizon. Many novel statistical methods have been introduced to address large volatility matrix estimation problems from a high-dimensional Ito process with microstructural noise contamination. Their asymptotic theories require sub-Gaussian or some finite high-order moments assumptions for observed log-returns. These assumptions are at odd with the heavy tail phenomenon that is pandemic in financial stock returns and new procedures are needed to mitigate the influence of heavy tails. In this paper, we introduce the Huber loss function with a diverging threshold to develop a robust realized volatility estimation. We show that it has the sub-Gaussian concentration around the volatility with only finite fourth moments of observed log-returns. With the proposed robust estimator as input, we further regularize it by using the principal orthogonal component thresholding (POET) procedure to estimate the large volatility matrix that admits an approximate factor structure. We establish the asymptotic theories for such low-rank plus sparse matrices. The simulation study is conducted to check the finite sample performance of the proposed estimation methods.

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 A Comparative Study on Large Multivariate Volatility Matrix Modeling for High frequency Financial Data written by Dongchen Jiang and published by . This book was released on 2015 with total page 80 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: Modeling and forecasting the volatilities of high-frequency data observed on the prices of financial assets are vibrant research areas in econometrics and statistics. However, most of the available methods are not directly applicable when the number of assets involved is large, due to the lack of accuracy in estimating high-dimensional matrices. This paper compared two methodologies of vast volatility matrix estimation for high-frequency data. One is to estimate the Average Realized Volatility Matrix and to regularize it by banding and thresholding. In this method, first we select grids as pre-sampling frequencies, construct a realized volatility matrix using previous tick method according to each pre-sampling frequency and then take the average of the constructed realized volatility matrices as the stage one estimator, which we call the ARVM estimator. Then we regularize the ARVM estimator to yield good consistent estimators of the large integrated volatility matrix. We consider two regularizations: thresholding and banding. The other is Dynamic Conditional Correlation (DCC) which can be estimated for two stage, where in the rst stage univariate GARCH models are estimated for each residual series, and in the second stage, the residuals are used to estimate the parameters of the dynamic correlation. Asymptotic theory for the two proposed methodologies shows that the estimator are consistent. In numerical studies, the proposed two methodologies are applied to simulated data set and real high-frequency prices from top 100 S & P 500 stocks according to the trading volume over a period of 3 months, 64 trading days in 2013. From the perfomances of estimators, the conclusion is that TARVM estimator performs better than DCC volatility matrix. And its largest eigenvalues are more stable than those of DCC model so that it is more approriable in eigen-based anaylsis.

Download or read book Handbook of HydroInformatics written by Saeid Eslamian and published by Elsevier. This book was released on 2022-11-30 with total page 484 pages. Available in PDF, EPUB and Kindle. Book excerpt: Classic Soft-Computing Techniques is the first volume of the three, in the Handbook of HydroInformatics series.? Through this comprehensive, 34-chapters work, the contributors explore the difference between traditional computing, also known as hard computing, and soft computing, which is based on the importance given to issues like precision, certainty and rigor. The chapters go on to define fundamentally classic soft-computing techniques such as Artificial Neural Network, Fuzzy Logic, Genetic Algorithm, Supporting Vector Machine, Ant-Colony Based Simulation, Bat Algorithm, Decision Tree Algorithm, Firefly Algorithm, Fish Habitat Analysis, Game Theory, Hybrid Cuckoo–Harmony Search Algorithm, Honey-Bee Mating Optimization, Imperialist Competitive Algorithm, Relevance Vector Machine, etc.?It is a fully comprehensive handbook providing all the information needed around classic soft-computing techniques. This volume is a true interdisciplinary work, and the audience includes postgraduates and early career researchers interested in Computer Science, Mathematical Science, Applied Science, Earth and Geoscience, Geography, Civil Engineering, Engineering, Water Science, Atmospheric Science, Social Science, Environment Science, Natural Resources, and Chemical Engineering. Key insights from global contributors in the fields of data management research, climate change and resilience, insufficient data problem, etc. Offers applied examples and case studies in each chapter, providing the reader with real world scenarios for comparison. Introduces classic soft-computing techniques, necessary for a range of disciplines.

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 2011-11-16 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 The Elements of Financial Econometrics written by Jianqing Fan and published by Cambridge University Press. This book was released on 2017-03-23 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: A compact, master's-level textbook on financial econometrics, focusing on methodology and including real financial data illustrations throughout. The mathematical level is purposely kept moderate, allowing the power of the quantitative methods to be understood without too much technical detail.

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 A Factor and Vector AR Model on Analyzing High Dimension Volatility for High frequency Financial Data written by Pengfei Li and published by . This book was released on 2007 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Large Volatility Matrix Analysis Using Global and National Factor Models written by Sung Hoon Choi and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Several large volatility matrix inference procedures have been developed, based on the latent factor model. They often assumed that there are a few of common factors, which can account for volatility dynamics. However, several studies have demonstrated the presence of local factors. In particular, when analyzing the global stock market, we often observe that nation-specific factors explain their own country's volatility dynamics. To account for this, we propose the Double Principal Orthogonal complEment Thresholding (Double-POET) method, based on multi-level factor models, and also establish its asymptotic properties. Furthermore, we demonstrate the drawback of using the regular principal orthogonal component thresholding (POET) when the local factor structure exists. We also describe the blessing of dimensionality using Double-POET for local covariance matrix estimation. Finally, we investigate the performance of the Double-POET estimator in an out-of-sample portfolio allocation study using international stocks from 20 financial markets.

Download or read book High Frequency Data Frequency Domain Inference and Volatility Forecasting written by Jonathan H. Wright and published by . This book was released on 1999 with total page 38 pages. Available in PDF, EPUB and Kindle. Book excerpt: While it is clear that the volatility of asset returns is serially correlated, there is no general agreement as to the most appropriate parametric model for characterizing this temporal dependence. In this paper, we propose a simple way of modeling financial market volatility using high frequency data. The method avoids using a tight parametric model, by instead simply fitting a long autoregression to log-squared, squared or absolute high frequency returns. This can either be estimated by the usual time domain method, or alternatively the autoregressive coefficients can be backed out from the smoothed periodogram estimate of the spectrum of log-squared, squared or absolute returns. We show how this approach can be used to construct volatility forecasts, which compare favorably with some leading alternatives in an out-of-sample forecasting exercise.

Download or read book Macroeconomic Forecasting in the Era of Big Data written by Peter Fuleky and published by Springer Nature. This book was released on 2019-11-28 with total page 716 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book surveys big data tools used in macroeconomic forecasting and addresses related econometric issues, including how to capture dynamic relationships among variables; how to select parsimonious models; how to deal with model uncertainty, instability, non-stationarity, and mixed frequency data; and how to evaluate forecasts, among others. Each chapter is self-contained with references, and provides solid background information, while also reviewing the latest advances in the field. Accordingly, the book offers a valuable resource for researchers, professional forecasters, and students of quantitative economics.

Download or read book Generalized Dynamic Factor Model GARCH Exploiting Multivariate Information for Univariate Prediction written by and published by . This book was released on 2007 with total page 15 pages. Available in PDF, EPUB and Kindle. Book excerpt: We propose a new model for volatility forecasting which combines the Generalized Dynamic Factor Model (GDFM) and the GARCH model. The GDFM, applied to a large number of series, captures the multivariate information and disentangles the common and the idiosyncratic part of each series of returns. In this financial analysis, both these components are modeled as a GARCH.We compare GDFM+GARCH and standard GARCH performance on two samples up to 171 series, providing one-step-ahead volatility predictions of returns. The GDFM+GARCH model outperforms the standard GARCH in most cases. These results are robust with respect to different volatility proxies. -- Dynamic Factors ; GARCH ; volatility forecasting

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 2012-03-22 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 Factor High frequency Based Volatility HEAVY Models written by Kevin Sheppard and published by . This book was released on 2014 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Realized GARCH written by Zhuo Huang and published by . This book was released on 2010 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: GARCH models have been successful in modeling financial returns. Still, much is to be gained by incorporating a realized measure of volatility in these models. In this thesis, we introduce a new framework for the joint modeling of returns and realized measures of volatility. A key feature of the Realized GARCH framework is a measurement equation that relates the observed realized measure to latent volatility. The new framework fills the gap between two lines of research on volatility modeling: GARCH and high frequency data. There are three major advantages of the Realized GARCH framework. First, the new framework nests most GARCH models as special cases and is, in many ways, a natural extension of standard GARCH models. The models with linear and log-linear specifications retain the simplicity and tractability of the classical GARCH framework; they imply an ARMA structure for the conditional variance and for the realized measures of volatility; and models in this class are parsimonious and simple to estimate. The measurement equation facilitates a simple modeling of the dependence between returns and future volatility that is commonly referred to as the leverage effect. Second, by incorporating the realized measures into the model, which are based on high frequency data and are much more accurate measurements for integrated volatility than daily squared returns, the Realized GARCH models provide a better performance in modeling and forecasting volatility. An empirical application with DJIA stocks and an exchange traded index fund shows that a simple Realized GARCH structure leads to substantial improvements in the empirical fit over to the standard GARCH model. This is true in-sample as well as out-of-sample. Moreover, the point estimates are remarkably similar across the different time series. Third, the measurement equation enables us to obtain additional insights on the bias and variance of different realized measures. Realized EGARCH model further extends the Realized GARCH model by reparameterizing the model and allowing different impacts of the leverage effect and residual measurement error on the conditional variance. The empirical results are in general consistent with the theoretical results in high frequency data literature and give practical guidance about how to use realized measures directly. The Realized EGARCH model is also applied to the exchange traded fund S & P500 index to study the volatility shocks during the financial crisis. We use this model to zoom into the events during the 2007-2009 period, and the model produces a daily series of volatility shocks. We link the announcements of events to large positive and negative volatility shocks.