Abstract: In the first half of this century, special attention was given to two features of the business cycle: the comovement of many individual economic series and the different behavior of the economy during expansions and contractions. Recent theoretical and empirical research has revived interest in each attribute separately, and we survey this work. Notable empirical contributions are dynamic factor models that have a single common macroeconomic factor and nonlinear regime-switching models of a macroeconomic aggregate. We conduct an empirical synthesis that incorporates both of these features. It is desirable to know the facts before attempting to explain them; hence, the attractiveness of organizing business-cycle regularities within a model-free framework. During the first half of this century, much research was devoted to obtaining just such an empirical characterization of the business cycle. The most prominent example of this work

Hidden Markov Models (HMMs) are statistical models of sequential data that have been used successfully in many machine learning applications, especially for speech recognition. Furthermore, in the last few years, many new and promising probabilistic models related to HMMs have been proposed. We first summarize the basics of HMMs, and then review several recent related learning algorithms and extensions of HMMs, including in particular hybrids of HMMs with artificial neural networks, Input-Output HMMs (which are conditional HMMs using neural networks to compute probabilities), weighted transducers, variable-length Markov models and Markov switching state-space models. Finally, we discuss some of the challenges of future research in this very active area. 1 Introduction Hidden Markov Models (HMMs) are statistical models of sequential data that have been used successfully in many applications in artificial intelligence, pattern recognition, speech recognition, and modeling of biological ...

especially grateful for the thoughtful and thorough comments of the referee which greatly improved the paper. Geert Bekaert thanks the NSF for financial support.

Abstract: The turmoil in the capital markets in 1997 and 1998 has highlighted the need for systematic stress testing of banks ’ portfolios, including both their trading and lending books. We propose that underlying macroeconomic volatility is a key part of a useful conceptual framework for stress testing credit portfolios, and that credit migration matrices provide the specific linkages between underlying macroeconomic conditions and asset quality. Credit migration matrices, which characterize the expected changes in credit quality of obligors, are cardinal inputs to many applications, including portfolio risk assessment, modeling the term structure of credit risk premia, and pricing of credit derivatives. They are also an integral part of many of the credit portfolio models used by financial institutions. By separating the economy into two states or regimes, expansion and contraction, and conditioning the migration matrix on these states, we show that the loss distribution of credit portfolios can differ greatly, as can the concomitant level of economic capital to be assigned to a bank.

This paper derives the moments for a range of Markov switching models. We characterize in detail the patterns of volatility, skewness and kurtosis that these models can produce as a function of the transition probabilities and parameters of the underlying state densities entering the switching process. The autocovariance of the level and squares of time series generated by Markov switching processes is also derived and we use these results to shed light on the relationship between volatility clustering, regime switches and structural breaks in time series models. JEL Code: C1. Key Words: Markov Switching, Higher Order Moments, Mixtures of Normals, Volatility Clustering. # Two anonymous referees and an associate editor provided many useful suggestions for improvements of the paper. Discussions with Jim Hamilton and Martin Sola also were very helpful. + Financial Markets Group, Houghton Street, London WC2A 2AE, England. 1 1. Introduction Markov switching models have become increasing...

Functionals of a two-parameter integrated periodogram have been used for a long time for detecting changes in the spectral distribution of a stationary sequence. The bases for these results are functional central limit theorems for the integrated periodogram having as limit a Gaussian field. In the case of GARCH(p; q) processes a statistic closely related to the integrated periodogram can be used for the purpose of change detection in the model. We derive a central limit theorem for this statistic under the hypothesis of a GARCH(p; q) sequence with a finite 4th moment. When applied to real-life time series our method gives clear evidence of the fast pace of change in the data. One of the straightforward conclusions of our study is the infeasibility of modeling long return series with one GARCH model. The parameters of the model must be updated and we propose a method to detect when the update is needed. Our study supports the hypothesis of global non-stationarity of the return time ser...

In this paper we give the theoretical basis of a possible explanation for two stylized facts observed in long log-return series: the long range dependence (LRD) in volatility and the integrated GARCH (IGARCH). Both these eects can be theoretically explained if one assumes that the data is non-stationary.

This paper introduces four models of conditional heteroscedasticity that contain markov switching parameters to examine their multi-period stock-market volatility forecasts as predictions of options-implied volatilities. The volatility model that best predicts the behavior of the options-implied volatilities allows the student-t degrees-of-freedom parameter to switch such that the conditional variance and kurtosis are subject to discrete shifts. The half-life of the most leptokurtic state is estimated to be a week, so expected market volatility reverts to near-normal levels fairly quickly following a spike. keywords: conditional heteroscedasticity; asset price volatility; kurtosis; markov switching 1 1. Introduction Volatility clustering is a well-documented feature of financial rates of return: Price changes that are large in magnitude tend to occur in bunches rather than with equal spacing. A natural question is how long financial markets will remain volatile, because volatility...

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