Download or read book GEL Estimation for Heavy Tailed GARCH Models with Robust Empirical Likelihood Inference written by Jonathan B. Hill and published by . This book was released on 2013 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: We construct a Generalized Empirical Likelihood estimator for a GARCH(1,1) model with a possibly heavy tailed error. The estimator imbeds tail-trimmed estimating equations allowing for over-identifying conditions, asymptotic normality, efficiency and empirical likelihood based confidence regions for very heavy-tailed random volatility data. We show the implied probabilities from the tail-trimmed Continuously Updated Estimator elevate weight for usable large values, assign large but not maximum weight to extreme observations, and give the lowest weight to non-leverage points. Finally, we present robust versions of Generalized Empirical Likelihood Ratio, Wald, and Lagrange Multiplier tests, and an efficient and heavy tail robust moment estimator with an application to the estimation of a conditionally heteroscedastic asset's expected shortfall.
Download or read book Robust Estimation and Inference for Heavy Tailed GARCH written by Jonathan B. Hill and published by . This book was released on 2014 with total page 43 pages. Available in PDF, EPUB and Kindle. Book excerpt: We develop two new estimators for a general class of stationary GARCH models with possibly heavy tailed asymmetrically distributed errors, covering processes with symmetric and asymmetric feedback like GARCH, Asymmetric GARCH, VGARCH and Quadratic GARCH. The first estimator arises from negligibly trimming QML criterion equations according to error extremes. The second imbeds negligibly transformed errors into QML score equations for a Method of Moments estimator. In this case we exploit a sub-class of redescending transforms that includes tail-trimming and functions popular in the robust estimation literature, and we re-center the transformed errors to minimize small sample bias. The negligible transforms allow both identification of the true parameter and asymptotic normality. We present a consistent estimator of the covariance matrix that permits classic inference without knowledge of the rate of convergence. A simulation study shows both of our estimators trump existing ones for sharpness and approximate normality including QML, Log-LAD, and two types of non-Gaussian QML (Laplace and Power-Law). Finally, we apply the tail-trimmed QML estimator to financial data.
Download or read book Heavy Tails And Copulas Topics In Dependence Modelling In Economics And Finance written by Rustam Ibragimov and published by World Scientific. This book was released on 2017-02-24 with total page 303 pages. Available in PDF, EPUB and Kindle. Book excerpt: 'Overall, the book is highly technical, including full mathematical proofs of the results stated. Potential readers are post-graduate students or researchers in Quantitative Risk Management willing to have a manual with the state-of-the-art on portfolio diversification and risk aggregation with heavy tails, including the fundamental theorems as well as collateral (but most useful) results on majorization and copula theory.'Quantitative Finance This book offers a unified approach to the study of crises, large fluctuations, dependence and contagion effects in economics and finance. It covers important topics in statistical modeling and estimation, which combine the notions of copulas and heavy tails — two particularly valuable tools of today's research in economics, finance, econometrics and other fields — in order to provide a new way of thinking about such vital problems as diversification of risk and propagation of crises through financial markets due to contagion phenomena, among others. The aim is to arm today's economists with a toolbox suited for analyzing multivariate data with many outliers and with arbitrary dependence patterns. The methods and topics discussed and used in the book include, in particular, majorization theory, heavy-tailed distributions and copula functions — all applied to study robustness of economic, financial and statistical models, and estimation methods to heavy tails and dependence.
Download or read book Robustness in Econometrics written by Vladik Kreinovich and published by Springer. This book was released on 2017-02-11 with total page 693 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents recent research on robustness in econometrics. Robust data processing techniques – i.e., techniques that yield results minimally affected by outliers – and their applications to real-life economic and financial situations are the main focus of this book. The book also discusses applications of more traditional statistical techniques to econometric problems. Econometrics is a branch of economics that uses mathematical (especially statistical) methods to analyze economic systems, to forecast economic and financial dynamics, and to develop strategies for achieving desirable economic performance. In day-by-day data, we often encounter outliers that do not reflect the long-term economic trends, e.g., unexpected and abrupt fluctuations. As such, it is important to develop robust data processing techniques that can accommodate these fluctuations.
Download or read book Advances in Mathematics and Applications written by Carlile Lavor and published by Springer. This book was released on 2018-09-07 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book celebrates the 50th anniversary of the Institute of Mathematics, Statistics and Scientific Computing (IMECC) of the University of Campinas, Brazil, by offering reviews of selected research developed at one of the most prestigious mathematics institutes in Latin America. Written by senior professors at the IMECC, it covers topics in pure and applied mathematics and statistics ranging from differential geometry, dynamical systems, Lie groups, and partial differential equations to computational optimization, mathematical physics, stochastic process, time series, and more. A report on the challenges and opportunities of research in applied mathematics - a highly active field of research in the country - and highlights of the Institute since its foundation in 1968 completes this historical volume, which is unveiled in the same year that the International Mathematical Union (IMU) names Brazil as a member of the Group V of countries with the most relevant contributions in mathematics.
Download or read book Robust Estimation for the Orthogonal GARCH Model written by Farhat Iqbal and published by . This book was released on 2013 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, we propose a class of robust M-estimators for the orthogonal generalized autoregressive conditional heteroscedastic (GARCH) model. The method involves the estimation of only univariate GARCH models and hence easy to estimate and does not put additional constraints on the model. The forecasting performance of the class of robust estimators in predicting correlation and value-at-risk using various evaluation measures are investigated. We found empirical evidences of the better predictive potential of estimators such as least absolute deviation and B-estimator over the widely used quasi-maximum likelihood estimator when the error distribution is heavy-tailed and asymmetric. Applications to real data sets are also presented.
Download or read book Quasi Maximum Likelihood Estimation of GARCH Models with Heavy Tailed Likelihoods written by Jianqing Fan and published by . This book was released on 2012 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The non-Gaussian maximum likelihood estimator is frequently used in GARCH models with the intention of capturing the heavy-tailed returns. However, unless the parametric likelihood family contains the true likelihood, the estimator is inconsistent due to density misspecification. To correct this bias, we identify an unknown scale parameter that is critical to the identification, and propose a two-step quasi maximum likelihood procedure with non-Gaussian likelihood functions. This novel approach is consistent and asymptotically normal under weak moment conditions. Moreover, it achieves better efficiency than the Gaussian alternative, particularly when the innovation error has heavy tails. We also summarize and compare the values of the scale parameter and the asymptotic efficiency for estimators based on different choices of likelihood functions with an increasing level of heaviness in the innovation tails. Numerical studies confirm the advantages of the proposed approach.
Download or read book Research Papers in Statistical Inference for Time Series and Related Models written by Yan Liu and published by Springer Nature. This book was released on 2023-05-31 with total page 591 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book compiles theoretical developments on statistical inference for time series and related models in honor of Masanobu Taniguchi's 70th birthday. It covers models such as long-range dependence models, nonlinear conditionally heteroscedastic time series, locally stationary processes, integer-valued time series, Lévy Processes, complex-valued time series, categorical time series, exclusive topic models, and copula models. Many cutting-edge methods such as empirical likelihood methods, quantile regression, portmanteau tests, rank-based inference, change-point detection, testing for the goodness-of-fit, higher-order asymptotic expansion, minimum contrast estimation, optimal transportation, and topological methods are proposed, considered, or applied to complex data based on the statistical inference for stochastic processes. The performances of these methods are illustrated by a variety of data analyses. This collection of original papers provides the reader with comprehensive and state-of-the-art theoretical works on time series and related models. It contains deep and profound treatments of the asymptotic theory of statistical inference. In addition, many specialized methodologies based on the asymptotic theory are presented in a simple way for a wide variety of statistical models. This Festschrift finds its core audiences in statistics, signal processing, and econometrics.
Download or read book Empirical Likelihood Inference for the Accelerated Failure Time Model Via Kendall Estimating Equation written by Yinghua Lu and published by . This book was released on 2009 with total page 55 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this thesis, we study two methods for inference of parameters in the accelerated failure time model with right censoring data. One is the Wald-type method, which involves parameter estimation. The other one is empirical likelihood method, which is based on the asymptotic distribution of likelihood ratio. We employ a monotone censored data version of Kendall estimating equation, and construct confidence intervals from both methods. In the simulation studies, we compare the empirical likelihood (EL) and the Wald-type procedure in terms of coverage accuracy and average length of confidence intervals. It is concluded that the empirical likelihood method has a better performance. We also compare the EL for Kendall's rank regression estimator with the EL for other well known estimators and find advantages of the EL for Kendall estimator for small size sample. Finally, a real clinical trial data is used for the purpose of illustration.
Download or read book Efficient and Robust Estimation of GARCH Models written by X. Jiang and published by . This book was released on 2015 with total page 12 pages. Available in PDF, EPUB and Kindle. Book excerpt: Generalized autoregressive conditional heteroscedastic (GARCH) models have been a powerful tool for modeling volatility. In this paper, we propose an efficient and robust method for estimating the parameters of GARCH models. This method involves a sequence of weights and takes a data-driven weighting scheme to maximize the asymptotic efficiency of the estimators. Under regularity conditions, we establish asymptotic distributions of the proposed estimators for a variety of heavy- or light-tailed error distributions. Simulations endorse our theoretical results. Our approach is applied to analyze the S&P 500 Composite index in the U.S. financial market and run some regression diagnostics to validate the fitted model.
Download or read book The Empirical Likelihood MPEC Approach to Demand Estimation written by Christopher T. Conlon and published by . This book was released on 2013 with total page 39 pages. Available in PDF, EPUB and Kindle. Book excerpt: The family of Generalized Empirical Likelihood (GEL) estimators provide a number of potential advantages relative to Generalized Method of Moments (GMM) estimators. While it is well known these estimators share an asymptotic distribution, the GEL estimators may perform better in finite sample, particularly in the case of many weak instruments. A relatively new literature has documented that finite-sample bias in the demand estimation problem of Berry, Levinsohn, and Pakes (1995) is often large, especially in the absence of exogenous cost shifting instruments. This paper provides a formulation for a computationally tractable GEL estimator based on the MPEC method of Su and Judd (2012) and adapts it to the BLP problem. When compared to GMM, the GEL estimator performs substantially better, reducing the bias by as much as 90%. Furthermore, it is possible to use analytic bias correction to reduce the bias even more and obtain accurate estimates with relatively small numbers of markets.
Download or read book Heavy Tails and Copulas written by Rustam Ibragimov and published by . This book was released on 2017 with total page 303 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This book offers a unified approach to the study of crises, large fluctuations, dependence and contagion effects in economics and finance. It covers important topics in statistical modeling and estimation, which combine the notions of copulas and heavy tails — two particularly valuable tools of today's research in economics, finance, econometrics and other fields — in order to provide a new way of thinking about such vital problems as diversification of risk and propagation of crises through financial markets due to contagion phenomena, among others. The aim is to arm today's economists with a toolbox suited for analyzing multivariate data with many outliers and with arbitrary dependence patterns. The methods and topics discussed and used in the book include, in particular, majorization theory, heavy-tailed distributions and copula functions — all applied to study robustness of economic, financial and statistical models, and estimation methods to heavy tails and dependence."--Publisher's website.
Download or read book Quantitative Methods for Economics and Finance written by J.E. Trinidad-Segovia and published by MDPI. This book was released on 2021-02-12 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a collection of papers for the Special Issue “Quantitative Methods for Economics and Finance” of the journal Mathematics. This Special Issue reflects on the latest developments in different fields of economics and finance where mathematics plays a significant role. The book gathers 19 papers on topics such as volatility clusters and volatility dynamic, forecasting, stocks, indexes, cryptocurrencies and commodities, trade agreements, the relationship between volume and price, trading strategies, efficiency, regression, utility models, fraud prediction, or intertemporal choice.
Download or read book Non Linear Time Series Models in Empirical Finance written by Philip Hans Franses and published by Cambridge University Press. This book was released on 2000-07-27 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: This 2000 volume reviews non-linear time series models, and their applications to financial markets.
Download or read book FDIC Quarterly written by and published by . This book was released on 2009 with total page 38 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Data Analysis written by Wolfgang A. Gaul and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 517 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Data Analysis" in the broadest sense is the general term for a field of activities of ever-increasing importance in a time called the information age. It covers new areas with such trendy labels as, e.g., data mining or web mining as well as traditional directions emphazising, e.g., classification or knowledge organization. Leading researchers in data analysis have contributed to this volume and delivered papers on aspects ranging from scientific modeling to practical application. They have devoted their latest contributions to a book edited to honor a colleague and friend, Hans-Hermann Bock, who has been active in this field for nearly thirty years.
Download or read book Estimation Inference and Specification Analysis written by Halbert White and published by Cambridge University Press. This book was released on 1996-06-28 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book examines the consequences of misspecifications for the interpretation of likelihood-based methods of statistical estimation and interference. The analysis concludes with an examination of methods by which the possibility of misspecification can be empirically investigated.
