3,576 research outputs found
Introduction to finite mixtures
Mixture models have been around for over 150 years, as an intuitively simple
and practical tool for enriching the collection of probability distributions
available for modelling data. In this chapter we describe the basic ideas of
the subject, present several alternative representations and perspectives on
these models, and discuss some of the elements of inference about the unknowns
in the models. Our focus is on the simplest set-up, of finite mixture models,
but we discuss also how various simplifying assumptions can be relaxed to
generate the rich landscape of modelling and inference ideas traversed in the
rest of this book.Comment: 14 pages, 7 figures, A chapter prepared for the forthcoming Handbook
of Mixture Analysis. V2 corrects a small but important typographical error,
and makes other minor edits; V3 makes further minor corrections and updates
following review; V4 corrects algorithmic details in sec 4.1 and 4.2, and
removes typo
Decoding the Australian electricity market: new evidence from three-regime hidden semi-Markov model
The hidden semi-Markov model (HSMM) is more flexible than the hidden Markov model (HMM). As an extension of the HMM, the sojourn time distribution in the HSMM can be explicitly specified by any distribution, either nonparametric or parametric, facilitating the modelling for the stylised features of electricity prices, such as the short-lived spike and the time-varying mean. By using a three-regime HSMM, this paper investigates the hidden regimes in five Australian States (Queensland, New South Wales, Victoria, South Australia, and Tasmania), spanning the period from June 8, 2008 to July 3, 2016. Based on the estimation results, we find evidence that the three hidden regimes correspond to a low-price regime, a high-price regime, and a spike regime. Running the decoding algorithm, the analysis systemically finds the timing of the three regimes, and thus, we link the empirical results to the policy changes in the Australian National Electricity Market. We further discuss the contributing factors for the different characteristics of the Australian electricity markets at the state-level
Markov-switching generalized additive models
We consider Markov-switching regression models, i.e. models for time series
regression analyses where the functional relationship between covariates and
response is subject to regime switching controlled by an unobservable Markov
chain. Building on the powerful hidden Markov model machinery and the methods
for penalized B-splines routinely used in regression analyses, we develop a
framework for nonparametrically estimating the functional form of the effect of
the covariates in such a regression model, assuming an additive structure of
the predictor. The resulting class of Markov-switching generalized additive
models is immensely flexible, and contains as special cases the common
parametric Markov-switching regression models and also generalized additive and
generalized linear models. The feasibility of the suggested maximum penalized
likelihood approach is demonstrated by simulation and further illustrated by
modelling how energy price in Spain depends on the Euro/Dollar exchange rate
Hierarchical hidden Markov structure for dynamic correlations: the hierarchical RSDC model.
This paper presents a new multivariate GARCH model with time-varying conditional correlation structure which is a generalization of the Regime Switching Dynamic Correlation (RSDC) of Pelletier (2006). This model, which we name Hierarchical RSDC, is building with the hierarchical generalization of the hidden Markov model introduced by Fine et al. (1998). This can be viewed graphically as a tree-structure with different types of states. The first are called production states and they can emit observations, as in the classical Markov-Switching approach. The second are called abstract states. They can't emit observations but establish vertical and horizontal probabilities that define the dynamic of the hidden hierarchical structure. The main gain of this approach compared to the classical Markov-Switching model is to increase the granularity of the regimes. Our model is also compared to the new Double Smooth Transition Conditional Correlation GARCH model (DSTCC), a STAR approach for dynamic correlations proposed by Silvennoinen and TerÀsvirta (2007). The reason is that under certain assumptions, the DSTCC and our model represent two classical competing approaches to modeling regime switching. We also perform Monte-Carlo simulations and we apply the model to two empirical applications studying the conditional correlations of selected stock returns. Results show that the Hierarchical RSDC provides a good measure of the correlations and also has an interesting explanatory power.Multivariate GARCH; Dynamic correlations; Regime switching; Markov chain; Hidden Markov models; Hierarchical Hidden Markov models
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