Hidden Markov Models, usually referred to as HMMs, are one of the most successful concepts in statistical modeling conceived and analyzed in the last 40 years. They belong to the stochastic mixture models family and have been broadly implemented in numerous sectors to address the problem of data model fitting and forecasting. Their structure usually is comprised by an observed sequence which is conditioned on an underlying hidden (unobserved) process. This way HMMs provide flexibility to address various complicated problems and can be implemented for modeling univariate and multivariate financial time series. Moreover, based on current literature, economic variables exhibit patterns dependent on different economic regimes which can be successfully captured by HMMs. Their parsimonious structure and attractive properties along with the existence of efficient algorithms for their estimation were the main drivers for the selection of HMM as the main topic of this thesis. Consequently, in this thesis we thoroughly investigate HMMs and their capabilities to simulate financial systems. The contribution of this study is threefold: First we perform an extensive review of HMM theory and applications. Our aim is to summarize the most significant applications of HMM with special focus in the field of finance. We offer a thorough and compact summary of the uses and the results of HMM in the last 40 years. Secondly, we extend the framework of HMMs by proposing a theoretical variation, injecting greater flexibility in their structure. Based on bibliography, in many real-world scenarios the modeled data entail temporal dynamics the patterns of which change over time. We address this problem by proposing a novel HMM formulation, treating temporal dependencies as latent variables over which inference is performed. Specifically, we introduce a hierarchical graphical model comprising two hidden layers: on the first layer, we postulate a chain of latent observation-emitting states, the temporal dependencies between which may change over time; on the second layer, we postulate a latent first-order Markov chain modeling the evolution of temporal dynamics (dependence jumps) pertaining to the first-layer latent process. As a result of this construction, our method allows for effectively modeling non-homogeneous observed financial data. Finally in the third part of this thesis we investigate the HMM efficiency in the problem of corporate credit scoring. We propose a novel corporate credit rating system based on Student’s-t hidden Markov models (SHMMs). Corporate credit scoring is widely used by financial institutions for portfolio risk management, and for pricing financial products designed for corporations. In addition, from a regulatory perspective, internal rating models are commonly used for establishing a more risk-sensitive capital adequacy framework for financial institutions. We evaluate our method against other state of the art statistical techniques like Neural Networks, SVM, and logistic regression and conclude that SHMM offer significant improved forecasting capabilities.
A Structural Parametrization of the Brain Using Hidden Markov Models-Based Paths in Alzheimer’s Disease
