Further applications of higher-order Markov chains and developments in regime-switching models

We consider a higher-order hidden Markov models (HMM), also called weak HMM (WHMM), to capture the regime-switching and memory properties of financial time series. A technique of transforming a WHMM into a regular HMM is employed, which in turn enables the development of recursive filters. With the use of the change of reference probability measure methodology and EM algorithm, a dynamic estimation of model parameters is obtained. Several applications and extensions were investigated. WHMM is adopted in describing the evolution of asset prices and its performance is examined through a forecasting analysis. This is extended to the case when the drift and volatility components of the logreturns are modulated by two independent WHMMs that are not necessarily having the same number of states. Numerical experiment is conducted based on simulated data to demonstrate the ability of our estimation approach in recovering the “true” model parameters. The analogue of recursive filtering and parameter estimation to handle multivariate data is also established. Some aspects of statistical inference arising from model implementation such as the assessment of model adequacy and goodness of fit are examined and addressed. The usefulness of the WHMM framework is tested on an asset allocation problem whereby investors determine the optimal investment strategy for the next time step through the results of the algorithm procedure. As an application in the modelling of yield curves, it is shown that the WHMM, with its memory-capturing mechanism, outperforms the usual HMM. A mean-reverting interest rate model is further developed whereby its parameters are modulated by a WHMM along with the formulation of a self-tuning parameter estimation. Finally, we propose an inverse Stieltjes moment approach to solve the inverse problem of calibration inherent in an HMM-based regime-switching set-up

Estimation of Hidden Markov Models and Their Applications in Finance

Movements of financial variables exhibit extreme fluctuations during periods of economic crisis and times of market uncertainty. They are also affected by institutional policies and intervention of regulatory authorities. These structural changes driving prices and other economic indicators can be captured reasonably by models featuring regime-switching capabilities. Hidden Markov models (HMM) modulating the model parameters to incorporate such regime-switching dynamics have been put forward in recent years, but many of them could still be further improved. In this research, we aim to address some of the inadequacies of previous regime-switching models in terms of their capacity to provide better forecasts and efficiency in estimating parameters. New models are developed, and their corresponding filtering results are obtained and tested on financial data sets. The contributions of this research work include the following: (i) Recursive filtering algorithms are constructed for a regime-switching financial model consistent with no-arbitrage pricing. An application to the filtering and forecasting of futures prices under a multivariate set-up is presented. (ii) The modelling of risk due to market and funding liquidity is considered by capturing the joint dynamics of three time series (Treasury-Eurodollar spread, VIX and S\&P 500 spread-derived metric), which mirror liquidity levels in the financial markets. HMM filters under a multi-regime mean- reverting model are established. (iii) Kalman filtering techniques and the change of reference probability-based filtering methods are integrated to obtain hybrid algorithms. A pairs trading investment strategy is supported by the combined power of both HMM and Kalman filters. It is shown that an investor is able to benefit from the proposed interplay of the two filtering methods. (iv) A zero-delay HMM is devised for the evolution of multivariate foreign exchange rate data under a high-frequency trading environment. Recursive filters for quantities that are functions of a Markov chain are derived, which in turn provide optimal parameter estimates. (v) An algorithm is designed for the efficient calculation of the joint probability function for the occupation time in a Markov-modulated model for asset returns under a general number of economic regimes. The algorithm is constructed with accessible implementation and practical considerations in mind

Fast human behavior analysis for scene understanding

Human behavior analysis has become an active topic of great interest and relevance for a number of applications and areas of research. The research in recent years has been considerably driven by the growing level of criminal behavior in large urban areas and increase of terroristic actions. Also, accurate behavior studies have been applied to sports analysis systems and are emerging in healthcare. When compared to conventional action recognition used in security applications, human behavior analysis techniques designed for embedded applications should satisfy the following technical requirements: (1) Behavior analysis should provide scalable and robust results; (2) High-processing efficiency to achieve (near) real-time operation with low-cost hardware; (3) Extensibility for multiple-camera setup including 3-D modeling to facilitate human behavior understanding and description in various events. The key to our problem statement is that we intend to improve behavior analysis performance while preserving the efficiency of the designed techniques, to allow implementation in embedded environments. More specifically, we look into (1) fast multi-level algorithms incorporating specific domain knowledge, and (2) 3-D configuration techniques for overall enhanced performance. If possible, we explore the performance of the current behavior-analysis techniques for improving accuracy and scalability. To fulfill the above technical requirements and tackle the research problems, we propose a flexible behavior-analysis framework consisting of three processing-layers: (1) pixel-based processing (background modeling with pixel labeling), (2) object-based modeling (human detection, tracking and posture analysis), and (3) event-based analysis (semantic event understanding). In Chapter 3, we specifically contribute to the analysis of individual human behavior. A novel body representation is proposed for posture classification based on a silhouette feature. Only pure binary-shape information is used for posture classification without texture/color or any explicit body models. To this end, we have studied an efficient HV-PCA shape-based descriptor with temporal modeling, which achieves a posture-recognition accuracy rate of about 86% and outperforms other existing proposals. As our human motion scheme is efficient and achieves a fast performance (6-8 frames/second), it enables a fast surveillance system or further analysis of human behavior. In addition, a body-part detection approach is presented. The color and body ratio are combined to provide clues for human body detection and classification. The conventional assumption of up-right body posture is not required. Afterwards, we design and construct a specific framework for fast algorithms and apply them in two applications: tennis sports analysis and surveillance. Chapter 4 deals with tennis sports analysis and presents an automatic real-time system for multi-level analysis of tennis video sequences. First, we employ a 3-D camera model to bridge the pixel-level, object-level and scene-level of tennis sports analysis. Second, a weighted linear model combining the visual cues in the real-world domain is proposed to identify various events. The experimentally found event extraction rate of the system is about 90%. Also, audio signals are combined to enhance the scene analysis performance. The complete proposed application is efficient enough to obtain a real-time or near real-time performance (2-3 frames/second for 720×576 resolution, and 5-7 frames/second for 320×240 resolution, with a P-IV PC running at 3GHz). Chapter 5 addresses surveillance and presents a full real-time behavior-analysis framework, featuring layers at pixel, object, event and visualization level. More specifically, this framework captures the human motion, classifies its posture, infers the semantic event exploiting interaction modeling, and performs the 3-D scene reconstruction. We have introduced our system design based on a specific software architecture, by employing the well-known "4+1" view model. In addition, human behavior analysis algorithms are directly designed for real-time operation and embedded in an experimental runtime AV content-analysis architecture. This executable system is designed to be generic for multiple streaming applications with component-based architectures. To evaluate the performance, we have applied this networked system in a single-camera setup. The experimental platform operates with two Pentium Quadcore engines (2.33 GHz) and 4-GB memory. Performance evaluations have shown that this networked framework is efficient and achieves a fast performance (13-15 frames/second) for monocular video sequences. Moreover, a dual-camera setup is tested within the behavior-analysis framework. After automatic camera calibration is conducted, the 3-D reconstruction and communication among different cameras are achieved. The extra view in the multi-camera setup improves the human tracking and event detection in case of occlusion. This extension of multiple-view fusion improves the event-based semantic analysis by 8.3-16.7% in accuracy rate. The detailed studies of two experimental intelligent applications, i.e., tennis sports analysis and surveillance, have proven their value in several extensive tests in the framework of the European Candela and Cantata ITEA research programs, where our proposed system has demonstrated competitive performance with respect to accuracy and efficiency

A hidden Markov model for statistical arbitrage in international crude oil futures markets

In this work, we study statistical arbitrage strategies in international crude oil futures markets. We analyse strategies that extend classical pairs trading strategies, considering the two benchmark crude oil futures (Brent and WTI) together with the newly introduced Shanghai crude oil futures. We document that the time series of these three futures prices are cointegrated and we model the resulting cointegration spread by a mean-reverting regime-switching process modulated by a hidden Markov chain. By relying on our stochastic model and applying online filter-based parameter estimators, we implement and test a number of statistical arbitrage strategies. Our analysis reveals that statistical arbitrage strategies involving the Shanghai crude oil futures are profitable even under conservative levels of transaction costs and over different time periods. On the contrary, statistical arbitrage strategies involving the three traditional crude oil futures (Brent, WTI, Dubai) do not yield profitable investment opportunities. Our findings suggest that the Shanghai futures, which has already become the benchmark for the Chinese domestic crude oil market, can be a valuable asset for international investors

Applications of hidden Markov models in financial modelling

This thesis was submitted for the degree of Doctor of Philosophy and was awarded by Brunel University.Various models driven by a hidden Markov chain in discrete or continuous time are developed to capture the stylised features of market variables whose levels or values constitute as the underliers of financial derivative contracts or investment portfolios. Since the parameters are switching regimes, the changes and developments in the economy as soon as they arise are readily reflected in these models. The change of probability measure technique and the EM algorithm are fundamental techniques utilised in the optimal parameter estimation. Recursive adaptive filters for the state of the Markov chain and other auxiliary processes related to the Markov chain are derived which in turn yield self-tuning dynamic financial models. A hidden Markov model (HMM)-based modelling set-up for commodity prices is developed and the predictability of the gold market under this setting is examined. An Ornstein-Uhlenbeck (OU) model with HMM parameters is proposed and under this set-up, we address two statistical inference issues: the sensitivity of the model to small changes in parameter estimates and the selection of the optimal number of states. The extended OU model is implemented on a data set of 30-day Canadian T-bill yields. An exponential of a Markov-switching OU process plus a compound Poisson process is put forward as a model for the evolution of electricity spot prices. Using a data set compiled by Nord Pool, we illustrate the vast improvements gained in incorporating regimes in the model. A multivariate HMM is employed as a framework in providing the solutions of two asset allocation problems; one involves the mean-variance utility function and the other entails the CVaR constraint. Finally, the valuation of credit default swaps highlights the important considerations necessitated by pricing in a regime-switching environment. Certain numerical schemes are applied to obtain approximations for the default probabilities and swap rates.Brunel Research Initiative and Enterprise Fund (BRIEF) and European Union (Marie Curie Fellowship

Direct Speech Reconstruction From Articulatory Sensor Data by Machine Learning

This paper describes a technique that generates speech acoustics from articulator movements. Our motivation is to help people who can no longer speak following laryngectomy, a procedure that is carried out tens of thousands of times per year in the Western world. Our method for sensing articulator movement, permanent magnetic articulography, relies on small, unobtrusive magnets attached to the lips and tongue. Changes in magnetic field caused by magnet movements are sensed and form the input to a process that is trained to estimate speech acoustics. In the experiments reported here this “Direct Synthesis” technique is developed for normal speakers, with glued-on magnets, allowing us to train with parallel sensor and acoustic data. We describe three machine learning techniques for this task, based on Gaussian mixture models, deep neural networks, and recurrent neural networks (RNNs). We evaluate our techniques with objective acoustic distortion measures and subjective listening tests over spoken sentences read from novels (the CMU Arctic corpus). Our results show that the best performing technique is a bidirectional RNN (BiRNN), which employs both past and future contexts to predict the acoustics from the sensor data. BiRNNs are not suitable for synthesis in real time but fixed-lag RNNs give similar results and, because they only look a little way into the future, overcome this problem. Listening tests show that the speech produced by this method has a natural quality that preserves the identity of the speaker. Furthermore, we obtain up to 92% intelligibility on the challenging CMU Arctic material. To our knowledge, these are the best results obtained for a silent-speech system without a restricted vocabulary and with an unobtrusive device that delivers audio in close to real time. This work promises to lead to a technology that truly will give people whose larynx has been removed their voices back

Coordinated Multi-Agent Imitation Learning

We study the problem of imitation learning from demonstrations of multiple coordinating agents. One key challenge in this setting is that learning a good model of coordination can be difficult, since coordination is often implicit in the demonstrations and must be inferred as a latent variable. We propose a joint approach that simultaneously learns a latent coordination model along with the individual policies. In particular, our method integrates unsupervised structure learning with conventional imitation learning. We illustrate the power of our approach on a difficult problem of learning multiple policies for fine-grained behavior modeling in team sports, where different players occupy different roles in the coordinated team strategy. We show that having a coordination model to infer the roles of players yields substantially improved imitation loss compared to conventional baselines.Comment: International Conference on Machine Learning 201

Valuation and Risk Management of Some Longevity and P&C Insurance Products

Numerous insurance products linked to risky assets have emerged rapidly in the last couple of decades. These products have option-embedded features and typically involve at least two risk factors, namely interest and mortality risks. The need for models to capture risk factors\u27 behaviours accurately is enormous and critical for insurance companies. The primary objective of this thesis is to develop pricing and hedging frameworks for option-embedded longevity products addressing correlated risk factors. Various methods are employed to facilitate the computation of prices and risk measures of longevity products including those with maturity benefits. Furthermore, in order to be prepared for the implementation of the new International Financial Reporting Standards (IFRS) 17, the thesis\u27s secondary objective is to provide a methodology for computing risk margins under the impending regulatory requirements. This is demonstrated using a property and casualty (P&C) insurance example and taking advantage of P&C data availability. To accomplish the above-mentioned objectives, five self-contained but related research works are undertaken and described as follows. (i) A pricing framework for annuities is constructed, where interest and mortality rates are both stochastic and dependent. The short-rate process and the force of mortality follow the two-factor Hull-White model and Lee-Carter model, respectively. (ii) The framework in (i) is further developed by adopting the Cox-Ingersoll-Ross model for the short-rate process to price guarantee annuity options (GAOs). The change of measure technique together with the comonotonicity theory is utilised to facilitate the computation of GAO prices. (iii) A further modelling framework extension is attained by considering a two-decrement model for GAO\u27s valuation and risk measurement. Interest rate, mortality and lapse risks are assumed correlated and they are all modelled as affine-diffusion processes. Risk measures are calculated via the moment-based density method. (iv) We introduce a regime-switching set up for the valuation of guaranteed minimum maturity benefits (GMMBs). A hidden Markov model (HMM) modulates the evolution of risk processes and the HMM-based filtering technique is employed to generate the risk-factor models\u27 parameter estimates. An analytical expression for GMMB value is derived with the aid of the change of measure technique in combination with a Fourier-transform approach. (v) Finally, a paid-incurred chain method is customised to model Ontario\u27s automobile claim development triangular data set over a 15-year period, and the moment-based density method is applied to approximate the distributions of outstanding claim liabilities. The risk margins are determined through risk measures as prescribed by the IFRS 17. Sensitivity analysis is performed for risk margins using the bootstrap method

A novel lip geometry approach for audio-visual speech recognition

By identifying lip movements and characterizing their associations with speech sounds, the performance of speech recognition systems can be improved, particularly when operating in noisy environments. Various method have been studied by research group around the world to incorporate lip movements into speech recognition in recent years, however exactly how best to incorporate the additional visual information is still not known. This study aims to extend the knowledge of relationships between visual and speech information specifically using lip geometry information due to its robustness to head rotation and the fewer number of features required to represent movement. A new method has been developed to extract lip geometry information, to perform classification and to integrate visual and speech modalities. This thesis makes several contributions. First, this work presents a new method to extract lip geometry features using the combination of a skin colour filter, a border following algorithm and a convex hull approach. The proposed method was found to improve lip shape extraction performance compared to existing approaches. Lip geometry features including height, width, ratio, area, perimeter and various combinations of these features were evaluated to determine which performs best when representing speech in the visual domain. Second, a novel template matching technique able to adapt dynamic differences in the way words are uttered by speakers has been developed, which determines the best fit of an unseen feature signal to those stored in a database template. Third, following on evaluation of integration strategies, a novel method has been developed based on alternative decision fusion strategy, in which the outcome from the visual and speech modality is chosen by measuring the quality of audio based on kurtosis and skewness analysis and driven by white noise confusion. Finally, the performance of the new methods introduced in this work are evaluated using the CUAVE and LUNA-V data corpora under a range of different signal to noise ratio conditions using the NOISEX-92 dataset