Analysis of the Likelihood Function for Markov-Switching VAR(CH) Models

Analysis of the Likelihood Function for Markov-Switching VAR(CH) Models
Author: Maddalena Cavicchioli
Publisher:
Total Pages: 0
Release: 2014
Genre:
ISBN:

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In this work, we give simple matrix formulae for maximum likelihood estimates of parameters in a broad class of vector autoregressions subject to Markovian changes in regime. This allows us to determine explicitly the asymptotic variance-covariance matrix of the estimators, giving a concrete possibility for the use of the classical testing procedures. In the context of multivariate autoregressive conditional heteroskedastic models with changes in regime, we provide formulae for the analytic derivatives of the log likelihood. Then we prove the consistency of some maximum likelihood estimators and give some formulae for the asymptotic variance of the different estimators.

Advances in Markov-Switching Models

Advances in Markov-Switching Models
Author: James D. Hamilton
Publisher: Springer Science & Business Media
Total Pages: 267
Release: 2013-06-29
Genre: Business & Economics
ISBN: 3642511821

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This book is a collection of state-of-the-art papers on the properties of business cycles and financial analysis. The individual contributions cover new advances in Markov-switching models with applications to business cycle research and finance. The introduction surveys the existing methods and new results of the last decade. Individual chapters study features of the U. S. and European business cycles with particular focus on the role of monetary policy, oil shocks and co movements among key variables. The short-run versus long-run consequences of an economic recession are also discussed. Another area that is featured is an extensive analysis of currency crises and the possibility of bubbles or fads in stock prices. A concluding chapter offers useful new results on testing for this kind of regime-switching behaviour. Overall, the book provides a state-of-the-art over view of new directions in methods and results for estimation and inference based on the use of Markov-switching time-series analysis. A special feature of the book is that it includes an illustration of a wide range of applications based on a common methodology. It is expected that the theme of the book will be of particular interest to the macroeconomics readers as well as econometrics professionals, scholars and graduate students. We wish to express our gratitude to the authors for their strong contributions and the reviewers for their assistance and careful attention to detail in their reports.

Maximum Likelihood Estimation of the Markov-Switching GARCH Model

Maximum Likelihood Estimation of the Markov-Switching GARCH Model
Author: Maciej Augustyniak
Publisher:
Total Pages: 32
Release: 2016
Genre:
ISBN:

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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.

Maximum Likelihood Estimation of the Markov-Switching GARCH Model Based on a General Collapsing Procedure

Maximum Likelihood Estimation of the Markov-Switching GARCH Model Based on a General Collapsing Procedure
Author: Maciej Augustyniak
Publisher:
Total Pages: 33
Release: 2017
Genre:
ISBN:

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The Markov-switching GARCH model allows for a GARCH structure with time-varying parameters. This flexibility is unfortunately undermined by a path dependence problem which complicates the parameter estimation process. This problem led to the development of computationally intensive estimation methods and to simpler techniques based on an approximation of the model, known as collapsing procedures. This article develops an original algorithm to conduct maximum likelihood inference in the Markov-switching GARCH model, generalizing and improving previously proposed collapsing approaches. A new relationship between particle filtering and collapsing procedures is established which reveals that this algorithm corresponds to a deterministic particle filter. Simulation and empirical studies show that the proposed method allows for a fast and accurate estimation of the model.

GARCH Models

GARCH Models
Author: Christian Francq
Publisher: John Wiley & Sons
Total Pages: 504
Release: 2019-03-19
Genre: Mathematics
ISBN: 1119313562

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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.

Financial Risk Management with Bayesian Estimation of GARCH Models

Financial Risk Management with Bayesian Estimation of GARCH Models
Author: David Ardia
Publisher: Springer Science & Business Media
Total Pages: 206
Release: 2008-05-08
Genre: Business & Economics
ISBN: 3540786570

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This book presents in detail methodologies for the Bayesian estimation of sing- regime and regime-switching GARCH models. These models are widespread and essential tools in n ancial econometrics and have, until recently, mainly been estimated using the classical Maximum Likelihood technique. As this study aims to demonstrate, the Bayesian approach o ers an attractive alternative which enables small sample results, robust estimation, model discrimination and probabilistic statements on nonlinear functions of the model parameters. The author is indebted to numerous individuals for help in the preparation of this study. Primarily, I owe a great debt to Prof. Dr. Philippe J. Deschamps who inspired me to study Bayesian econometrics, suggested the subject, guided me under his supervision and encouraged my research. I would also like to thank Prof. Dr. Martin Wallmeier and my colleagues of the Department of Quantitative Economics, in particular Michael Beer, Roberto Cerratti and Gilles Kaltenrieder, for their useful comments and discussions. I am very indebted to my friends Carlos Ord as Criado, Julien A. Straubhaar, J er ^ ome Ph. A. Taillard and Mathieu Vuilleumier, for their support in the elds of economics, mathematics and statistics. Thanks also to my friend Kevin Barnes who helped with my English in this work. Finally, I am greatly indebted to my parents and grandparents for their support and encouragement while I was struggling with the writing of this thesis.

Analytical Derivatives for Markov Switching Models

Analytical Derivatives for Markov Switching Models
Author: Jeff Gable
Publisher:
Total Pages: 33
Release: 2008
Genre:
ISBN:

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This paper derives analytical gradients for a broad class of regime-switching models with Markovian state-transition probabilities. Such models are usually estimated by maximum likelihood methods, which require the derivatives of the likelihood function with respect to the parameter vector. These gradients are usually calculated by means of numerical techniques. The paper shows that analytical gradients considerably speed up maximum-likelihood estimation with no loss in accuracy. A sample program listing is included.

Handbook of Mixture Analysis

Handbook of Mixture Analysis
Author: Sylvia Fruhwirth-Schnatter
Publisher: CRC Press
Total Pages: 522
Release: 2019-01-04
Genre: Computers
ISBN: 0429508247

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Mixture models have been around for over 150 years, and they are found in many branches of statistical modelling, as a versatile and multifaceted tool. They can be applied to a wide range of data: univariate or multivariate, continuous or categorical, cross-sectional, time series, networks, and much more. Mixture analysis is a very active research topic in statistics and machine learning, with new developments in methodology and applications taking place all the time. The Handbook of Mixture Analysis is a very timely publication, presenting a broad overview of the methods and applications of this important field of research. It covers a wide array of topics, including the EM algorithm, Bayesian mixture models, model-based clustering, high-dimensional data, hidden Markov models, and applications in finance, genomics, and astronomy. Features: Provides a comprehensive overview of the methods and applications of mixture modelling and analysis Divided into three parts: Foundations and Methods; Mixture Modelling and Extensions; and Selected Applications Contains many worked examples using real data, together with computational implementation, to illustrate the methods described Includes contributions from the leading researchers in the field The Handbook of Mixture Analysis is targeted at graduate students and young researchers new to the field. It will also be an important reference for anyone working in this field, whether they are developing new methodology, or applying the models to real scientific problems.

Exact Markov Chain Monte Carlo with Likelihood Approximations for Functional Linear Models

Exact Markov Chain Monte Carlo with Likelihood Approximations for Functional Linear Models
Author: Corey James Smith
Publisher:
Total Pages:
Release: 2018
Genre: Bayesian statistical decision theory
ISBN:

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Functional data analysis is a branch of statistics that deals with the theory and analysis of data which may be comprised of functions in addition to scalar values. Here we consider the linear model that relates functional covariates to scalar responses. We introduce an exact MCMC algorithm which does not rely on likelihood evaluations to estimate the parameter function. The proposed method uses Barker's algorithm (as opposed to Metropolis-Hastings). Though Barker's has been shown to be asymptotically less efficient than Metropolis-Hastings, the form of its acceptance probability allows us to make the accept/reject decision efficiently without needing to evaluate the likelihood function. We utilize unbiased estimates of the log-likelihood function along with two nested Bernoulli factories to accomplish this. In addition, exact MCMC methods for logistic and Poisson regression settings with functional predictors are provided. These latter two models again feature Bernoulli factories and Barker's algorithm while also making use of debiasing techniques to aid in log-likelihood estimation.