Quasi-exact Approximation of Hidden Markov Chain Filters

This paper studies the application of exact simulation methods for multi-dimensional multiplicative noise stochastic differential equations to filtering. Stochastic differential equations with multiplicative noise naturally occur as Zakai equation in hidden Markov chain filtering. The paper proposes a quasi-exact approximation method for hidden Markov chain filters, which can be applied when discrete time approximations, such as the Euler scheme, may fail in practice.stochastic differential equations; Zakai equation; quasi-exact approximation; hidden Markov chain filtering

Convergence in distribution for filtering processes associated to Hidden Markov Models with densities

Consider a filtering process associated to a hidden Markov model with densities for which both the state space and the observation space are complete, separable, metric spaces. If the underlying, hidden Markov chain is strongly ergodic and the filtering process fulfills a certain coupling condition we prove that, in the limit, the distribution of the filtering process is independent of the initial distribution of the hidden Markov chain. If furthermore the hidden Markov chain is uniformly ergodic, then we prove that the filtering process converges in distribution.Comment: 54 pages revision. Rewritten introduction. Theorem 12.1 sharper than Theorem 16.1 (v1). Proofs and results reorganised. Example 18.3 (v1) exclude

Estimating ensemble flows on a hidden Markov chain

We propose a new framework to estimate the evolution of an ensemble of indistinguishable agents on a hidden Markov chain using only aggregate output data. This work can be viewed as an extension of the recent developments in optimal mass transport and Schr\"odinger bridges to the finite state space hidden Markov chain setting. The flow of the ensemble is estimated by solving a maximum likelihood problem, which has a convex formulation at the infinite-particle limit, and we develop a fast numerical algorithm for it. We illustrate in two numerical examples how this framework can be used to track the flow of identical and indistinguishable dynamical systems.Comment: 8 pages, 4 figure

Almost Sure Stabilization for Adaptive Controls of Regime-switching LQ Systems with A Hidden Markov Chain

This work is devoted to the almost sure stabilization of adaptive control systems that involve an unknown Markov chain. The control system displays continuous dynamics represented by differential equations and discrete events given by a hidden Markov chain. Different from previous work on stabilization of adaptive controlled systems with a hidden Markov chain, where average criteria were considered, this work focuses on the almost sure stabilization or sample path stabilization of the underlying processes. Under simple conditions, it is shown that as long as the feedback controls have linear growth in the continuous component, the resulting process is regular. Moreover, by appropriate choice of the Lyapunov functions, it is shown that the adaptive system is stabilizable almost surely. As a by-product, it is also established that the controlled process is positive recurrent

Forecasting Time Series Subject to Multiple Structural Breaks

This paper provides a novel approach to forecasting time series subject to discrete structural breaks. We propose a Bayesian estimation and prediction procedure that allows for the possibility of new breaks over the forecast horizon, taking account of the size and duration of past breaks (if any) by means of a hierarchical hidden Markov chain model. Predictions are formed by integrating over the hyper parameters from the meta distributions that characterize the stochastic break point process. In an application to US Treasury bill rates, we find that the method leads to better out-of-sample forecasts than alternative methods that ignore breaks, particularly at long horizons.structural breaks, forecasting, hierarchical hidden Markov chain model, Bayesian model averaging.

On Geometric Ergodicity of Skewed - SVCHARME models

Markov Chain Monte Carlo is repeatedly used to analyze the properties of intractable distributions in a convenient way. In this paper we derive conditions for geometric ergodicity of a general class of nonparametric stochastic volatility models with skewness driven by hidden Markov Chain with switching

Quasi-exact approximation of hidden Markov chain filters

This paper studies the application of exact simulation methods for multi-dimensional multiplicative noise stochastic differential equations to filtering. Stochastic differential equations with multiplicative noise naturally occur as Zakai equation in hidden Markov chain filtering. The paper proposes a quasi-exact approximation method for hidden Markov chain filters, which can be applied when discrete time approximations, such as the Euler scheme, may fail in practice

Dynamic factor analysis of carbon allowances prices: From classic Arbitrage Pricing Theory to Switching Regimes

The aim of this paper is to identify the fundamental factors that drive the allowances market and to built an APT-like model in order to provide accurate forecasts for CO2. We show that historic dependency patterns emphasis energy, natural gas, oil, coal and equity indexes as major factors driving the carbon allowances prices. There is strong evidence that model residuals are heavily tailed and asymmetric, thereby generalized hyperbolic distribution provides with the best fit results. Introducing dynamics inside the parameters of the APT model via a Hidden Markov Chain Model outperforms the results obtained with a static approach. Empirical results clearly indicate that this model could be used for price forecasting, that it is effective in and out of sample producing consisten results in allowances futures price prediction.Carbon, EUA, energy, Abritrage Pricing Theory, switching regimes, hidden Markov Chain Model, forecast.