The use of Markov-switching models to capture the volatility dynamics of financial time series has grown considerably during past years, in part because they give rise to a plausible interpretation of nonlinearities. Nevertheless, GARCH-type models remain ubiquitous in order to allow for nonlinearities associated with time-varying volatility. Existing methods of combining the two approaches are unsatisfactory, as they either suffer from severe estimation difficulties or else their dynamic properties are not well understood. In this article we present a new Markov-switching GARCH model that overcomes both of these problems. Dynamic properties are derived and their implications for the volatility process discussed. We argue that the disaggregation of the variance process offered by the new model is more plausible than in the existing variants. The approach is illustrated with several exchange rate return series. The results suggest that a promising volatility model is an independent switching GARCH process with a possibly skewed conditional mixture density.

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.

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.

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.

Specially selected from The New Palgrave Dictionary of Economics 2nd edition, each article within this compendium covers the fundamental themes within the discipline and is written by a leading practitioner in the field. A handy reference tool.

MSGtool is a MATLAB toolbox which provides a collection of functions for the simulation and estimation of a large variety of Markov Switching GARCH (MSG) models. Currently, the software integrates a method to select the best starting values for the estimation and a post-estimation analysis to ensure the convergence. The toolbox is very flexible a user-friendly with a large number possible options. In this paper, we give some illustrative examples.