Explicit-duration Markov Switching Models
Title | Explicit-duration Markov Switching Models PDF eBook |
Author | Silvia Chiappa |
Publisher | |
Pages | 83 |
Release | 2014 |
Genre | Markov processes |
ISBN | 9781601988317 |
Markov switching models (MSMs) are probabilistic models that employ multiple sets of parameters to describe different dynamic regimes that a time series may exhibit at different periods of time. The switching mechanism between regimes is controlled by unobserved random variables that form a first-order Markov chain. Explicit-duration MSMs contain additional variables that explicitly model the distribution of time spent in each regime. This allows to define duration distributions of any form, but also to impose complex dependence between the observations and to reset the dynamics to initial conditions. Models that focus on the first two properties are most commonly known as hidden semi-Markov models or segment models, whilst models that focus on the third property are most commonly known as changepoint models or reset models. In this monograph, we provide a description of explicit-duration modelling by categorizing the different approaches into three groups, which differ in encoding in the explicit-duration variables different information about regime change/reset boundaries. The approaches are described using the formalism of graphical models, which allows to graphically represent and assess statistical dependence and therefore to easily describe the structure of complex models and derive inference routines. The presentation is intended to be pedagogical, focusing on providing a characterization of the three groups in terms of model structure constraints and inference properties. The monograph is supplemented with a software package that contains most of the models and examples described. The material presented should be useful to both researchers wishing to learn about these models and researchers wishing to develop them further.
Explicit-Duration Markov Switching Models
Title | Explicit-Duration Markov Switching Models PDF eBook |
Author | Silvia Chiappa |
Publisher | Now Pub |
Pages | 102 |
Release | 2014-12-19 |
Genre | Computers |
ISBN | 9781601988300 |
Provides a simple and clear description of explicit duration modeling. The presentation focuses on making distinctions that help structure the space of models and in laying out inference and learning in a clear way. It is an ideal reference for students and researchers wishing to learn about these models and those looking to develop them further.
Time-Varying Transition Probabilities for Markov Regime Switching Models
Title | Time-Varying Transition Probabilities for Markov Regime Switching Models PDF eBook |
Author | Marco Bazzi |
Publisher | |
Pages | 0 |
Release | 2017 |
Genre | |
ISBN |
We propose a new Markov switching model with time-varying transitions probabilities. The novelty of our model is that the transition probabilities evolve over time by means of an observation driven model. The innovation of the time-varying probability is generated by the score of the predictive likelihood function. We show how the model dynamics can be readily interpreted. We investigate the performance of the model in a Monte Carlo study and show that the model is successful in estimating a range of different dynamic patterns for unobserved regime switching probabilities. We also illustrate the new methodology in an empirical setting by studying the dynamic mean and variance behaviour of US industrial production growth.
Analytical Derivatives for Markov Switching Models
Title | Analytical Derivatives for Markov Switching Models PDF eBook |
Author | Jeff Gable |
Publisher | |
Pages | 24 |
Release | 1995 |
Genre | Markov processes |
ISBN | 9780662236856 |
Synchronization of Markov Chains in Multivariate Regime-Switching Models
Title | Synchronization of Markov Chains in Multivariate Regime-Switching Models PDF eBook |
Author | Raphael Vial |
Publisher | |
Pages | 0 |
Release | 2015 |
Genre | |
ISBN |
Multivariate regime-switching presents an efficient way of jointly modeling the cyclical behavior of financial time series. Standard regime-switching models thereby a priori determine the relationship between the regime-switches of individual assets. These switches are usually assumed to be either perfectly synchronized or fully independent. However, neither assumption seems realistic in practice. This thesis develops a multivariate Markov regime-switching model to infer the actual degree of synchronization from the underlying data. This flexible model allows subgroups of assets to be driven by individual Markov chains. At the same time, these Markov chains underlie a dynamically changing degree of synchronization. In comparison to most existing solutions, this model is not restricted to bivariate analysis. To keep the model traceable, a novel factorization algorithm for the regime-dependent correlation matrix is formulated. This algorithm scales down the increase in parameters and presents an efficient way of ensuring positive semi-definite correlation matrices. The structure of the flexible regime-switching model is motivated by the initial synchronization analysis conducted in this thesis. The analysis of univariate regime-switching results shows that neither perfectly synchronized nor fully independent regime cycles are empirically observable. The synchronization of regime cycles tends to dynamically change over time. Some assets, however, might show more contemporaneous switching dynamics and can therefore be governed by a joint regime process. The empirical results for a sample of six international equity markets confirm the assumptions underlying this thesis. The flexible model reveals a stable synchronization factor, marked by one particular change in synchronization. The estimated parameters of this model closely cover the individual dynamics of their underlying assets and confirm the model's validity. Moreover, in some.
Time Varying Transition Probabilities for Markov Regime Switching Models
Title | Time Varying Transition Probabilities for Markov Regime Switching Models PDF eBook |
Author | Marco Bazzi |
Publisher | |
Pages | 26 |
Release | 2014 |
Genre | |
ISBN |
We propose a new Markov switching model with time varying probabilities for the transitions. The novelty of our model is that the transition probabilities evolve over time by means of an observation driven model. The innovation of the time varying probability is generated by the score of the predictive likelihood function. We show how the model dynamics can be readily interpreted. We investigate the performance of the model in a Monte Carlo study and show that the model is successful in estimating a range of different dynamic patterns for unobserved regime switching probabilities. We also illustrate the new methodology in an empirical setting by studying the dynamic mean and variance behavior of U.S. Industrial Production growth. We find empirical evidence of changes in the regime switching probabilities, with more persistence for high volatility regimes in the earlier part of the sample, and more persistence for low volatility regimes in the later part of the sample.
Hidden Markov Models for Time Series
Title | Hidden Markov Models for Time Series PDF eBook |
Author | Walter Zucchini |
Publisher | CRC Press |
Pages | 370 |
Release | 2017-12-19 |
Genre | Mathematics |
ISBN | 1482253844 |
Hidden Markov Models for Time Series: An Introduction Using R, Second Edition illustrates the great flexibility of hidden Markov models (HMMs) as general-purpose models for time series data. The book provides a broad understanding of the models and their uses. After presenting the basic model formulation, the book covers estimation, forecasting, decoding, prediction, model selection, and Bayesian inference for HMMs. Through examples and applications, the authors describe how to extend and generalize the basic model so that it can be applied in a rich variety of situations. The book demonstrates how HMMs can be applied to a wide range of types of time series: continuous-valued, circular, multivariate, binary, bounded and unbounded counts, and categorical observations. It also discusses how to employ the freely available computing environment R to carry out the computations. Features Presents an accessible overview of HMMs Explores a variety of applications in ecology, finance, epidemiology, climatology, and sociology Includes numerous theoretical and programming exercises Provides most of the analysed data sets online New to the second edition A total of five chapters on extensions, including HMMs for longitudinal data, hidden semi-Markov models and models with continuous-valued state process New case studies on animal movement, rainfall occurrence and capture-recapture data