This thesis develops new hidden Markov models and applies them to financial market and macroeconomic time series. Chapter 1 proposes a probabilistic model of the return distribution with rich and heterogeneous intra-regime dynamics. It focuses on the characteristics and dynamics of bear market rallies and bull market corrections, including, for example, the probability of transition from a bear market rally into a bull market versus back to the primary bear state. A Bayesian estimation approach accounts for parameter and regime uncertainty and provides probability statements regarding future regimes and returns. A Value-at-Risk example illustrates the economic value of our approach. Chapter 2 develops a new efficient approach to model and forecast time series data with an unknown number of change-points. The key is assuming a conjugate prior for the time-varying parameters which characterize each regime and treating the regime duration as a state variable. Conditional on this prior and the time-invariant parameters, the predictive density and the posterior of the change-points have closed forms. The conjugate prior is further modeled as hierarchical to exploit the information across regimes. This framework allows breaks in the variance, the regression coefficients or both. In addition to the time-invariant structural change probability, one extension assumes the regime duration has a Poisson distribution. A new Markov Chain Monte Carlo sampler draws the parameters from the posterior distribution efficiently. The model is applied to Canadian inflation time series. Chapter 3 proposes an infinite dimension Markov switching model to accommodate regime switching and structural break dynamics or a combination of both in a Bayesian framework. Two parallel hierarchical structures, one governing the transition probabilities and another governing the parameters of the conditional data density, keep the model parsimonious and improve forecasts. This nonparametric approach allows for regime persistence and estimates the number of states automatically. A global identification algorithm for structural changes versus regime switching is presented. Applications to U.S. real interest rates and inflation compare the new model to existing parametric alternatives. Besides identifying episodes of regime switching and structural breaks, the hierarchical distribution governing the parameters of the conditional data density provides significant gains to forecasting precision.

This thesis develops new hidden Markov models and applies them to financial market and macroeconomic time series. Chapter 1 proposes a probabilistic model of the return distribution with rich and heterogeneous intra-regime dynamics. It focuses on the characteristics and dynamics of bear market rallies and bull market corrections, including, for example, the probability of transition from a bear market rally into a bull market versus back to the primary bear state. A Bayesian estimation approach accounts for parameter and regime uncertainty and provides probability statements regarding future regimes and returns. A Value-at-Risk example illustrates the economic value of our approach. Chapter 2 develops a new efficient approach to model and forecast time series data with an unknown number of change-points. The key is assuming a conjugate prior for the time-varying parameters which characterize each regime and treating the regime duration as a state variable. Conditional on this prior and the time-invariant parameters, the predictive density and the posterior of the change-points have closed forms. The conjugate prior is further modeled as hierarchical to exploit the information across regimes. This framework allows breaks in the variance, the regression coefficients or both. In addition to the time-invariant structural change probability, one extension assumes the regime duration has a Poisson distribution. A new Markov Chain Monte Carlo sampler draws the parameters from the posterior distribution efficiently. The model is applied to Canadian inflation time series. Chapter 3 proposes an infinite dimension Markov switching model to accommodate regime switching and structural break dynamics or a combination of both in a Bayesian framework. Two parallel hierarchical structures, one governing the transition probabilities and another governing the parameters of the conditional data density, keep the model parsimonious and improve forecasts. This nonparametric approach allows for regime persistence and estimates the number of states automatically. A global identification algorithm for structural changes versus regime switching is presented. Applications to U.S. real interest rates and inflation compare the new model to existing parametric alternatives. Besides identifying episodes of regime switching and structural breaks, the hierarchical distribution governing the parameters of the conditional data density provides significant gains to forecasting precision.

This research focuses on Markov Decision Processes (MDP). MDP is one of the most important and challenging areas of Operations Research. Every day people make many decisions: today's decisions impact tomorrow's and tomorrow's will impact the ones made the day after. Problems in Engineering, Science, and Business often pose similar challenges: a large number of options and uncertainty about the future. MDP is one of the most powerful tools for solving such problems. There are several standard methods for finding optimal or approximately optimal policies for MDP. Approaches widely employed to solve MDP problems include value iteration and policy iteration. Although simple to implement, these approaches are, nevertheless, limited in the size of problems that can be solved, due to excessive computation required to find close-to-optimal solutions. My thesis proposes a new value iteration and modified policy iteration methods for classes of the expected discounted MDPs and average cost MDPs. We establish a class of operators that can be integrated into value iteration and modified policy iteration algorithms for Markov Decision Processes, so as to speed up the convergence of the iterative search. Application of these operators requires a little additional computation per iteration but reduces the number of iterations significantly. The development of the acceleration operators relies on two key properties of Markov operator, namely contraction mapping and monotonicity in a restricted region. Since Markov operators of the classical value iteration and modified policy iteration methods for average cost MDPs do not possess the contraction mapping property, for these models we restrict our study to average cost problems that can be formulated as the stochastic shortest path problem. The performance improvement is significant, while the implementation of the operator into the value iteration is trivial. Numerical studies show that the accelerated methods can be hundreds of times more efficient for solving MDP problems than the other known approaches. The computational savings can be significant especially when the discount factor approaches 1 and the transition probability matrix becomes dense, in which case the standard iterative algorithms suffer from slow convergence.

Les mots de Christoffel forment un sous-ensemble des mots de {x,y}*. Nous les présenterons dans ce mémoire de façon géométrique comme étant la discrétisation d'une droite allant de (0,0) à (a,b), avec a et b des entiers premiers entre eux, par un chemin dans IN2. Nous associerons ainsi les mots de Christoffel aux couples d'entiers premiers entre eux. Nous introduirons ensuite les triplets de Markoff comme étant les solutions de l'équation diophantienne a2+b2+c2 = 3abc. Un homomorphisme µ du monoïde libre {x,y}* dans SL2(Z) sera défini de la façon suivante : µx = (2 1 / 1 1) et µy = (5 2 / 2 1). Celui-ci nous permettra de définir la bijection suivante entre les mots de Christoffel et les triplets de Markoff : w = w1w2 → {⅓Tr(µw1), ⅓Tr (µw2), ⅓Tr(µw)}. Par la suite, nous introduirons l'arbre de Stern-Brocot, l'arbre de Christoffel et l’arbre de Markoff et nous montrerons l'équivalence entre tous ces arbres, et établirons des bijections canoniques entre eux. ______________________________________________________________________________ MOTS-CLÉS DE L’AUTEUR : Mots de Christoffel, triplets de Markoff, bijection, arbre de Christoffel, arbre de Markoff, arbre de Stern-Brocot.

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The objective of this thesis is to design and implement a speech recognition system for Mandarin names and phrases. This system utilizes Mel frequency cepstral coefficients, hidden Markov model and lexicon search strategy to select the phrase candidates. The experimental results indicate that for the speaker dependent case, a strategy incorporating overlapping frames and hybrid training can result in an improvement of 4%, 5%, 4% and 2% on the recognition rate for the Mandarin name, two-word, three-word and four-word phrase recognition systems respectively. Under Redhat Linux 9.0 operating system, any Mandarin name or phrase can be recognized within 2 seconds by a computer with Intel Celeron 2.4 GHz CPU.

Abstract A naturally system is usually modeled as a causal system, in which the present output is determined by the past inputs. In contrast, the noncausal system is modeled by the future inputs in addition to the past inputs, and is also less explored. In this thesis, we apply the noncausal modeling to the image restoration for the blurred images corrupted by additive white Gaussian noise. We applied three methods for our image deblurring problem. The first method is exploiting the compound Gauss-Markov image model, which has been proven useful in image restoration. The image is restored in two steps iteratively: restoring the line field by the assumed image field and restoring the image field by the just computed line field. The second method is to apply the Kalman filter using the above the compound Gauss-Markov image model and the line field. The third method is to apply the Kalman filter without using the line field. Our experiments have shown the second method to be the best among the three methods.

This thesis investigates the capacity expansion of distribution substation of each service area considering PV system penetration to achieve the cost effectiveness of substation investment to comply with the service reliability. With the land use planning of Kaohsiung City Government, the load density of each small area for the target year is derived according to the final floor area and development strength of the land base. The load forecasting of each small area is then solved by considering the load growth of each customer class and a Markov model is applied for the forecasting of solar energy, which is then included in the expansion planning of substations. The forecasting of annual peak loadings for each area over the future 20 years is performed by the time series method based on the historical load data and load type of customers served. The forced outage rate ¡]FOR¡^ of main transformers in the substations is used to solve the loss of load expectation¡]LOLE¡^ according to the peak loading of each service area. By this way, the capacity expansion planning of main transformers to meet the service reliability can therefore be derived. To further enhance the distribution system planning, the capacity transfer capability of main transformers and the tie line flow capacity between different areas are considered too. It is found that the expansion planning of main transformers by the proposed methodology can provide better cost effectiveness of transformer investment to satisfy the service reliability as well as the system peak loading.

Thesis Ph. D.--Applied mathematics--Åbo akademi university, 2005. / Bibliogr. p. 25-26.

Habilitation à diriger des recherches : Informatique : Rennes 1 : 1998. / Bibliogr. p.47-54.