A First Application of Independent Component Analysis to Extracting Structure from Stock Returns

This paper discusses the application of a modern signal processing technique known as independent component analysis (ICA) or blind source separation to multivariate financial time series such as a portfolio of stocks. The key idea of ICA is to linearly map the observed multivariate time series into a new space of statistically independent components (ICs). This can be viewed as a factorization of the portfolio since joint probabilities become simple products in the coordinate system of the ICs. We apply ICA to three years of daily returns of the 28 largest Japanese stocks and compare the results with those obtained using principal component analysis. The results indicate that the estimated ICs fall into two categories, (i) infrequent but large shocks (responsible for the major changes in the stock prices), and (ii) frequent smaller fluctuations (contributing little to the overall level of the stocks). We show that the overall stock price can be reconstructed surprisingly well by using a small number of thresholded weighted ICs. In contrast, when using shocks derived from principal components instead of independent components, the reconstructed price is less similar to the original one. Independent component analysis is a potentially powerful method of analyzing and understanding driving mechanisms in financial markets. There are further promising applications to risk management since ICA focuses on higher-order statistics.Information Systems Working Papers Serie

A First Application of Independent Component Analysis to Extracting Structure from Stock Returns

This paper discusses the application of a modern signal processing technique known as independent component analysis (ICA) or blind source separation to multivariate financial time series such as a portfolio of stocks. The key idea of ICA is to linearly map the observed multivariate time series into a new space of statistically independent components (ICs). This can be viewed as a factorization of the portfolio since joint probabilities become simple products in the coordinate system of the ICs. We apply ICA to three years of daily returns of the 28 largest Japanese stocks and compare the results with those obtained using principal component analysis. The results indicate that the estimated ICs fall into two categories, (i) infrequent but large shocks (responsible for the major changes in the stock prices), and (ii) frequent smaller fluctuations (contributing little to the overall level of the stocks). We show that the overall stock price can be reconstructed surprisingly well by using a small number of thresholded weighted ICs. In contrast, when using shocks derived from principal components instead of independent components, the reconstructed price is less similar to the original one. Independent component analysis is a potentially powerful method of analyzing and understanding driving mechanisms in financial markets. There are further promising applications to risk management since ICA focuses on higher-order statistics.Information Systems Working Papers Serie

Adaptive signal processing algorithms for noncircular complex data

The complex domain provides a natural processing framework for a large class of signals encountered in communications, radar, biomedical engineering and renewable energy. Statistical signal processing in C has traditionally been viewed as a straightforward extension of the corresponding algorithms in the real domain R, however, recent developments in augmented complex statistics show that, in general, this leads to under-modelling. This direct treatment of complex-valued signals has led to advances in so called widely linear modelling and the introduction of a generalised framework for the differentiability of both analytic and non-analytic complex and quaternion functions. In this thesis, supervised and blind complex adaptive algorithms capable of processing the generality of complex and quaternion signals (both circular and noncircular) in both noise-free and noisy environments are developed; their usefulness in real-world applications is demonstrated through case studies. The focus of this thesis is on the use of augmented statistics and widely linear modelling. The standard complex least mean square (CLMS) algorithm is extended to perform optimally for the generality of complex-valued signals, and is shown to outperform the CLMS algorithm. Next, extraction of latent complex-valued signals from large mixtures is addressed. This is achieved by developing several classes of complex blind source extraction algorithms based on fundamental signal properties such as smoothness, predictability and degree of Gaussianity, with the analysis of the existence and uniqueness of the solutions also provided. These algorithms are shown to facilitate real-time applications, such as those in brain computer interfacing (BCI). Due to their modified cost functions and the widely linear mixing model, this class of algorithms perform well in both noise-free and noisy environments. Next, based on a widely linear quaternion model, the FastICA algorithm is extended to the quaternion domain to provide separation of the generality of quaternion signals. The enhanced performances of the widely linear algorithms are illustrated in renewable energy and biomedical applications, in particular, for the prediction of wind profiles and extraction of artifacts from EEG recordings

Classification and detection of Critical Transitions: from theory to data

From population collapses to cell-fate decision, critical phenomena are abundant in complex real-world systems. Among modelling theories to address them, the critical transitions framework gained traction for its purpose of determining classes of critical mechanisms and identifying generic indicators to detect and alert them (“early warning signals”). This thesis contributes to such research field by elucidating its relevance within the systems biology landscape, by providing a systematic classification of leading mechanisms for critical transitions, and by assessing the theoretical and empirical performance of early warning signals. The thesis thus bridges general results concerning the critical transitions field – possibly applicable to multidisciplinary contexts – and specific applications in biology and epidemiology, towards the development of sound risk monitoring system

Wireless Network Analytics for Next Generation Spectrum Awareness

The importance of networks, in their broad sense, is rapidly and massively growing in modern-day society thanks to unprecedented communication capabilities offered by technology. In this context, the radio spectrum will be a primary resource to be preserved and not wasted. Therefore, the need for intelligent and automatic systems for in-depth spectrum analysis and monitoring will pave the way for a new set of opportunities and potential challenges. This thesis proposes a novel framework for automatic spectrum patrolling and the extraction of wireless network analytics. It aims to enhance the physical layer security of next generation wireless networks through the extraction and the analysis of dedicated analytical features. The framework consists of a spectrum sensing phase, carried out by a patrol composed of numerous radio-frequency (RF) sensing devices, followed by the extraction of a set of wireless network analytics. The methodology developed is blind, allowing spectrum sensing and analytics extraction of a network whose key features (i.e., number of nodes, physical layer signals, medium access protocol (MAC) and routing protocols) are unknown. Because of the wireless medium, over-the-air signals captured by the sensors are mixed; therefore, blind source separation (BSS) and measurement association are used to estimate the number of sources and separate the traffic patterns. After the separation, we put together a set of methodologies for extracting useful features of the wireless network, i.e., its logical topology, the application-level traffic patterns generated by the nodes, and their position. The whole framework is validated on an ad-hoc wireless network accounting for MAC protocol, packet collisions, nodes mobility, the spatial density of sensors, and channel impairments, such as path-loss, shadowing, and noise. The numerical results obtained by extensive and exhaustive simulations show that the proposed framework is consistent and can achieve the required performance

Analysis of Plasma Filaments with Fast Visible Imaging in the Mega Ampère Spherical Tokamak

The cross-field transport of particles in the scrape-off layer (SOL) of magnetic fusion devices is dominated by the convection of coherent filamentary plasma structures. In this thesis, we present a new technique for the analysis of filaments in fast visible camera data. The new technique operates by inverting the background subtracted emission in the camera images onto a basis set of uniformly emitting field line images, constructed using information from magnetic equilibrium reconstructions. The output of the inversion is a 2D mapping of emission parametrising the average intensity of field lines in the SOL by the coordinates of their intersection with the mid-plane. Filaments manifest in the inverted emission profile as blobs of raised emission. A filament detection technique has been developed to identify these regions of increased emission and fit them with 2D Gaussians. This yields the positions, widths and amplitudes of the filaments. A tracking algorithm is then applied to calculate the filaments velocities and lifetimes. Data from a synthetic camera diagnostic is used to assess the capabilities and limitations of the new technique and quantify its errors. This exercise shows it can detect ~36% of all filaments in the analysis region, corresponding to ~74% of filaments above the targeted amplitude threshold. This sensitivity is achieved with a true positive detection rate of 98.8%. Standard errors in the radial and toroidal positions of the filaments are estimated to be ~2 mm, while errors in the toroidal and radial widths are around ~3 mm and ~7 mm respectively. The shapes of the probability density functions (PDFs) of the filament parameters are also qualitatively recovered and the effect of filament overlap on filament amplitude measurements is investigated. Valuable insight is gained into effects from the non-orthogonality of the field line basis functions and the resulting spatial dependence of the measurement errors. Finally, the technique is applied to MAST data and compared to Langmuir probe measurements. Good agreement is found between the two diagnostics, including exponential waiting times and symmetrical conditionally averaged waveforms. Measurements of the PDFs of filament properties provide valuable inputs for analytic models of SOL transport and show filament lifetimes to be exponentially distributed. The depth of field of the technique enables measurement of the toroidal filament spacing, with results supporting the assertion that filaments are generated uniformly and independently, and are thus described by Poisson statistics underpinning several analytic models

Non-spurious correlations between genetic and linguistic diversities in the context of human evolution

This thesis concerns human diversity, arguing that it represents not just some form of noise, which must be filtered out in order to reach a deeper explanatory level, but the engine of human and language evolution, metaphorically put, the best gift Nature has made to us. This diversity must be understood in the context of (and must shape) human evolution, of which the Recent Out-of-Africa with Replacement model (ROA) is currently regarded, especially outside palaeoanthropology, as a true theory. It is argued, using data from palaeoanthropology, human population genetics, ancient DNA studies and primatology, that this model must be, at least, amended, and most probably, rejected, and its alternatives must be based on the concept of reticulation. The relationships between the genetic and linguistic diversities is complex, including interindividual genetic and behavioural differences (behaviour genetics) and inter-population differences due to common demographic, geographic and historic factors (spurious correlations), used to study (pre)historical processes. It is proposed that there also exist nonspurious correlations between genetic and linguistic diversities, due to genetic variants which can bias the process of language change, so that the probabilities of alternative linguistic states are altered. The particular hypothesis (formulated with Prof. D. R. Ladd) of a causal relationship between two human genes and one linguistic typological feature is supported by the statistical analysis of a vast database of 983 genetic variants and 26 linguistic features in 49 Old World populations, controlling for geography and known linguistic history. The general theory of non-spurious correlations between genetic and linguistic diversities is developed and its consequences and predictions analyzed. It will very probably profoundly impact our understanding of human diversity and will offer a firm footing for theories of language evolution and change. More specifically, through such a mechanism, gradual, accretionary models of language evolution are a natural consequence of post-ROA human evolutionary models. The unravellings of causal effects of inter-population genetic differences on linguistic states, mediated by complex processes of cultural evolution (biased iterated learning), will represent a major advance in our understanding of the relationship between cultural and genetic diversities, and will allow a better appreciation of this most fundamental and supremely valuable characteristic of humanity - its intrinsic diversity