Download or read book Efficiency Comparisons of Maximum Likelihood based Estimators in GARCH Models written by Gloria González-Rivera and published by . This book was released on 1998 with total page 36 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Efficiency Comparisons of Maximum Likelihood based Estimators in Garch Models and Testing for Density Functional Form written by Jeffrey Scott Racine and published by . This book was released on 1995 with total page 30 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Efficiency Comparison of Maximum Likelihood based Estimators in Garch Models written by Feike C. Drost and published by . This book was released on 1998 with total page 16 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 GARCH Models written by Christian Francq and published by John Wiley & Sons. This book was released on 2019-06-10 with total page 517 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides a comprehensive and updated study of GARCH models and their applications in finance, covering new developments in the discipline This book provides a comprehensive and systematic approach to understanding GARCH time series models and their applications whilst presenting the most advanced results concerning the theory and practical aspects of GARCH. The probability structure of standard GARCH models is studied in detail as well as statistical inference such as identification, estimation, and tests. The book also provides new coverage of several extensions such as multivariate models, looks at financial applications, and explores the very validation of the models used. GARCH Models: Structure, Statistical Inference and Financial Applications, 2nd Edition features a new chapter on Parameter-Driven Volatility Models, which covers Stochastic Volatility Models and Markov Switching Volatility Models. A second new chapter titled Alternative Models for the Conditional Variance contains a section on Stochastic Recurrence Equations and additional material on EGARCH, Log-GARCH, GAS, MIDAS, and intraday volatility models, among others. The book is also updated with a more complete discussion of multivariate GARCH; a new section on Cholesky GARCH; a larger emphasis on the inference of multivariate GARCH models; a new set of corrected problems available online; and an up-to-date list of references. Features up-to-date coverage of the current research in the probability, statistics, and econometric theory of GARCH models Covers significant developments in the field, especially in multivariate models Contains completely renewed chapters with new topics and results Handles both theoretical and applied aspects Applies to researchers in different fields (time series, econometrics, finance) Includes numerous illustrations and applications to real financial series Presents a large collection of exercises with corrections Supplemented by a supporting website featuring R codes, Fortran programs, data sets and Problems with corrections GARCH Models, 2nd Edition is an authoritative, state-of-the-art reference that is ideal for graduate students, researchers, and practitioners in business and finance seeking to broaden their skills of understanding of econometric time series models.
Download or read book Dependence in Probability and Statistics written by Patrice Bertail and published by Springer Science & Business Media. This book was released on 2006-09-24 with total page 491 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives an account of recent developments in the field of probability and statistics for dependent data. It covers a wide range of topics from Markov chain theory and weak dependence with an emphasis on some recent developments on dynamical systems, to strong dependence in times series and random fields. There is a section on statistical estimation problems and specific applications. The book is written as a succession of papers by field specialists, alternating general surveys, mostly at a level accessible to graduate students in probability and statistics, and more general research papers mainly suitable to researchers in the field.
Download or read book Nonparametric Statistical Methods And Related Topics A Festschrift In Honor Of Professor P K Bhattacharya On The Occasion Of His 80th Birthday written by Francisco J Samaniego and published by World Scientific. This book was released on 2011-09-16 with total page 479 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume consists of 22 research papers by leading researchers in Probability and Statistics. Many of the papers are focused on themes that Professor Bhattacharya has published on research. Topics of special interest include nonparametric inference, nonparametric curve fitting, linear model theory, Bayesian nonparametrics, change point problems, time series analysis and asymptotic theory.This volume presents state-of-the-art research in statistical theory, with an emphasis on nonparametric inference, linear model theory, time series analysis and asymptotic theory. It will serve as a valuable reference to the statistics research community as well as to practitioners who utilize methodology in these areas of emphasis.
Download or read book Handbook of Financial Time Series written by Torben Gustav Andersen and published by Springer Science & Business Media. This book was released on 2009-04-21 with total page 1045 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Handbook of Financial Time Series gives an up-to-date overview of the field and covers all relevant topics both from a statistical and an econometrical point of view. There are many fine contributions, and a preamble by Nobel Prize winner Robert F. Engle.
Download or read book Econometric Modelling with Time Series written by Vance Martin and published by Cambridge University Press. This book was released on 2013 with total page 925 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Maximum likelihood estimation is a general method for estimating the parameters of econometric models from observed data. The principle of maximum likelihood plays a central role in the exposition of this book, since a number of estimators used in econometrics can be derived within this framework. Examples include ordinary least squares, generalized least squares and full-information maximum likelihood. In deriving the maximum likelihood estimator, a key concept is the joint probability density function (pdf) of the observed random variables, yt. Maximum likelihood estimation requires that the following conditions are satisfied. (1) The form of the joint pdf of yt is known. (2) The specification of the moments of the joint pdf are known. (3) The joint pdf can be evaluated for all values of the parameters, 9. Parts ONE and TWO of this book deal with models in which all these conditions are satisfied. Part THREE investigates models in which these conditions are not satisfied and considers four important cases. First, if the distribution of yt is misspecified, resulting in both conditions 1 and 2 being violated, estimation is by quasi-maximum likelihood (Chapter 9). Second, if condition 1 is not satisfied, a generalized method of moments estimator (Chapter 10) is required. Third, if condition 2 is not satisfied, estimation relies on nonparametric methods (Chapter 11). Fourth, if condition 3 is violated, simulation-based estimation methods are used (Chapter 12). 1.2 Motivating Examples To highlight the role of probability distributions in maximum likelihood estimation, this section emphasizes the link between observed sample data and 4 The Maximum Likelihood Principle the probability distribution from which they are drawn"-- publisher.
Download or read book Estimation in Conditionally Heteroscedastic Time Series Models written by Daniel Straumann and published by Springer Science & Business Media. This book was released on 2006-01-27 with total page 239 pages. Available in PDF, EPUB and Kindle. Book excerpt: In his seminal 1982 paper, Robert F. Engle described a time series model with a time-varying volatility. Engle showed that this model, which he called ARCH (autoregressive conditionally heteroscedastic), is well-suited for the description of economic and financial price. Nowadays ARCH has been replaced by more general and more sophisticated models, such as GARCH (generalized autoregressive heteroscedastic). This monograph concentrates on mathematical statistical problems associated with fitting conditionally heteroscedastic time series models to data. This includes the classical statistical issues of consistency and limiting distribution of estimators. Particular attention is addressed to (quasi) maximum likelihood estimation and misspecified models, along to phenomena due to heavy-tailed innovations. The used methods are based on techniques applied to the analysis of stochastic recurrence equations. Proofs and arguments are given wherever possible in full mathematical rigour. Moreover, the theory is illustrated by examples and simulation studies.
Download or read book Maximum Likelihood Estimation of the Markov Switching GARCH Model written by Maciej Augustyniak and published by . This book was released on 2016 with total page 32 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Markov-switching GARCH model offers rich dynamics to model financial data. Estimating this path dependent model is a challenging task because exact computation of the likelihood is infeasible in practice. This difficulty led to estimation procedures either based on a simplification of the model or not dependent on the likelihood. There is no method available to obtain the maximum likelihood estimator without resorting to a modification of the model. A novel approach is developed based on both the Monte Carlo expectation-maximization algorithm and importance sampling to calculate the maximum likelihood estimator and asymptotic variance-covariance matrix of the Markov-switching GARCH model. Practical implementation of the proposed algorithm is discussed and its effectiveness is demonstrated in simulation and empirical studies.
Download or read book Journal of the American Statistical Association written by and published by . This book was released on 2009 with total page 896 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Estimating and Using GARCH Models with VIX Data for Option Valuation written by Juho Kanniainen and published by . This book was released on 2016 with total page 33 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper uses information on VIX to improve the empirical performance of GARCH models for pricing options on the S&P 500. In pricing multiple cross-sections of options, the models' performance can clearly be improved by extracting daily spot volatilities from the series of VIX rather than by linking spot volatility with different dates by using the series of the underlying's returns. Moreover, in contrast to traditional returns-based maximum likelihood estimation (MLE), a joint MLE with returns and VIX improves option pricing performance, and for NGARCH, joint MLE can yield empirically almost the same out-of-sample option pricing performance as direct calibration does to in-sample options, but without costly computations. Finally, consistently with the existing research, this paper finds that non-affine models clearly outperform affine models.
Download or read book Exact Maximum Likelihood Estimation of Observation driven Econometric Models written by Francis X. Diebold and published by . This book was released on 1996 with total page 38 pages. Available in PDF, EPUB and Kindle. Book excerpt: The possibility of exact maximum likelihood estimation of many observation-driven models remains an open question. Often only approximate maximum likelihood estimation is attempted, because the unconditional density needed for exact estimation is not known in closed form. Using simulation and nonparametric density estimation techniques that facilitate empirical likelihood evaluation, we develop an exact maximum likelihood procedure. We provide an illustrative application to the estimation of ARCH models, in which we compare the sampling properties of the exact estimator to those of several competitors. We find that, especially in situations of small samples and high persistence, efficiency gains are obtained. We conclude with a discussion of directions for future research, including application of our methods to panel data models.
Download or read book Consistency of Quasi Maximum Likelihood Estimators for Models with Conditional Heteroskedasticity written by Whitney K. Newey and published by . This book was released on 2008 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Virtually all empirical studies that assume a time-varying conditional variance use a quasi-maximum likelihood estimator (QMLE). If the density from which the likelihood is constructed is assumed to be Gaussian, the QMLE is known to be consistent under correct specification of both the conditional mean and conditional variance. We show that if both the assumed density and the true density are symmetric a QMLE remains consistent. If, however, either the assumed density or the true density is asymmetric, a QMLE is generally not consistent. To ensure that a QMLE is consistent under asymmetric densities, we include the conditional standard deviation as a regressor. We calculate the efficiency loss associated with the added regressor if the densities are symmetric and show that for a QMLE of the conditional variance parameters of a GARCH process there is no efficiency loss. Finally, we develop a test of consistency of a QMLE from the significance of the additional regressor.
Download or read book Method of Moments Estimation of GO GARCH Models written by Peter H. Boswijk and published by . This book was released on 2011 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Consistency of Quasi maximum Likelihood Estimators for the Regime switching GARCH Models written by Yingfu Xie and published by . This book was released on 2005 with total page 12 pages. Available in PDF, EPUB and Kindle. Book excerpt:
