Extraction of the underlying structure of systematic risk from non-Gaussian multivariate financial time series using independent component analysis: Evidence from the Mexican stock exchange

Regarding the problems related to multivariate non-Gaussianity of financial time series, i.e., unreliable results in extraction of underlying risk factors -via Principal Component Analysis or Factor Analysis-, we use Independent Component Analysis (ICA) to estimate the pervasive risk factors that explain the returns on stocks in the Mexican Stock Exchange. The extracted systematic risk factors are considered within a statistical definition of the Arbitrage Pricing Theory (APT), which is tested by means of a two-stage econometric methodology. Using the extracted factors, we find evidence of a suitable estimation via ICA and some results in favor of the APT.Peer ReviewedPostprint (published version

Characterization and processing of atrial fibrillation episodes by convolutive blind source separation algorithms and nonlinear analysis of spectral features

Las arritmias supraventriculares, en particular la fibrilación auricular (FA), son las enfermedades cardíacas más comúnmente encontradas en la práctica clínica rutinaria. La prevalencia de la FA es inferior al 1\% en la población menor de 60 años, pero aumenta de manera significativa a partir de los 70 años, acercándose al 10\% en los mayores de 80. El padecimiento de un episodio de FA sostenida, además de estar ligado a una mayor tasa de mortalidad, aumenta la probabilidad de sufrir tromboembolismo, infarto de miocardio y accidentes cerebrovasculares. Por otro lado, los episodios de FA paroxística, aquella que termina de manera espontánea, son los precursores de la FA sostenida, lo que suscita un alto interés entre la comunidad científica por conocer los mecanismos responsables de perpetuar o conducir a la terminación espontánea de los episodios de FA. El análisis del ECG de superficie es la técnica no invasiva más extendida en la diagnosis médica de las patologías cardíacas. Para utilizar el ECG como herramienta de estudio de la FA, se necesita separar la actividad auricular (AA) de las demás señales cardioeléctricas. En este sentido, las técnicas de Separación Ciega de Fuentes (BSS) son capaces de realizar un análisis estadístico multiderivación con el objetivo de recuperar un conjunto de fuentes cardioeléctricas independientes, entre las cuales se encuentra la AA. A la hora de abordar un problema de BSS, se hace necesario considerar un modelo de mezcla de las fuentes lo más ajustado posible a la realidad para poder desarrollar algoritmos matemáticos que lo resuelvan. Un modelo viable es aquel que supone mezclas lineales. Dentro del modelo de mezclas lineales se puede además hacer la restricción de que estas sean instantáneas. Este modelo de mezcla lineal instantánea es el utilizado en el Análisis de Componentes Independientes (ICA).Vayá Salort, C. (2010). Characterization and processing of atrial fibrillation episodes by convolutive blind source separation algorithms and nonlinear analysis of spectral features [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/8416Palanci

Blind Source Separation for the Processing of Contact-Less Biosignals

(Spatio-temporale) Blind Source Separation (BSS) eignet sich für die Verarbeitung von Multikanal-Messungen im Bereich der kontaktlosen Biosignalerfassung. Ziel der BSS ist dabei die Trennung von (z.B. kardialen) Nutzsignalen und Störsignalen typisch für die kontaktlosen Messtechniken. Das Potential der BSS kann praktisch nur ausgeschöpft werden, wenn (1) ein geeignetes BSS-Modell verwendet wird, welches der Komplexität der Multikanal-Messung gerecht wird und (2) die unbestimmte Permutation unter den BSS-Ausgangssignalen gelöst wird, d.h. das Nutzsignal praktisch automatisiert identifiziert werden kann. Die vorliegende Arbeit entwirft ein Framework, mit dessen Hilfe die Effizienz von BSS-Algorithmen im Kontext des kamera-basierten Photoplethysmogramms bewertet werden kann. Empfehlungen zur Auswahl bestimmter Algorithmen im Zusammenhang mit spezifischen Signal-Charakteristiken werden abgeleitet. Außerdem werden im Rahmen der Arbeit Konzepte für die automatisierte Kanalauswahl nach BSS im Bereich der kontaktlosen Messung des Elektrokardiogramms entwickelt und bewertet. Neuartige Algorithmen basierend auf Sparse Coding erwiesen sich dabei als besonders effizient im Vergleich zu Standard-Methoden.(Spatio-temporal) Blind Source Separation (BSS) provides a large potential to process distorted multichannel biosignal measurements in the context of novel contact-less recording techniques for separating distortions from the cardiac signal of interest. This potential can only be practically utilized (1) if a BSS model is applied that matches the complexity of the measurement, i.e. the signal mixture and (2) if permutation indeterminacy is solved among the BSS output components, i.e the component of interest can be practically selected. The present work, first, designs a framework to assess the efficacy of BSS algorithms in the context of the camera-based photoplethysmogram (cbPPG) and characterizes multiple BSS algorithms, accordingly. Algorithm selection recommendations for certain mixture characteristics are derived. Second, the present work develops and evaluates concepts to solve permutation indeterminacy for BSS outputs of contact-less electrocardiogram (ECG) recordings. The novel approach based on sparse coding is shown to outperform the existing concepts of higher order moments and frequency-domain features

Extraction of the underlying structure of systematic risk from Non-Gaussian multivariate financial time series using Independent Component Analysis. Evidence from the Mexican Stock Exchange

Regarding the problems related to multivariate non-Gaussianity of financial time series, i.e.,unreliable results in extraction of underlying risk factors - via Principal Component Analysis or Factor Analysis-, we use Independent Component Analysis (ICA) to estimate the pervasive risk factors that explain the returns on stocks in the Mexican Stock Exchange. The extracted systematic risk factors are considered within a statistical definition of the Arbitrage Pricing Theory (APT), which is tested by means of a two-stage econometric methodology. Using the extracted factors, we find evidence of a suitable estimation via ICA and some results in favor of the APT

Invariant Coordinate Selection and New Approaches for Independent Component Analysis

Tämän väitöskirjatyön tavoitteena oli tarkastella invarianttien koordinaattien valintaa ja tuoda uusia näkökulmia riippumattomien komponenttien analyysiin. Moniulotteisten tilastollisten menetelmien yhteydessä kysymykset invarianttisuudesta ja ekvivarianttisuudesta nousevat usein esille. Toisinaan tilastollisia menetelmiä joudutaan muokkaamaan, jotta niille voidaan löytää invariantti tai ekvivariantti vastine. Tämä voidaan tehdä esimerkiksi transformoimalla data invarianttiin koordinaattisysteemiin. Kahdessa väitöskirja-artikkelissa käsitellään invarianttien koordinaattien valintaa (ICS) ja ICS funktionaaleja. Moniulotteisen aineiston standardointia, ja ICS funktionaalien ja otossuureiden (asymptoottisia) ominaisuuksia tarkastellaan kattavasti. Myös moniulotteista huipukkuutta ja vinoutta käsitellään. ICS transformaatioiden sovellusalueista keskustellaan. Yksi tärkeä sovellusalue on riippumattomien komponenttien analyysi. Riippumattomien komponenttien analyysi (ICA) on hyvin ajankohtainen tutkimusalue ja sillä on useita käytännön sovelluskohteita. Riippumattomien komponenttien mallissa p-ulotteisen satunnaisvektorin alkioiden oletetaan olevan sellaisen tuntemattoman p-ulotteisen satunnaisvektorin alkioiden lineaarikombinaatioita, jonka alkiot ovat toisistaan riippumattomia. Riippumattomien komponenttien analyysissä tavoitteena on löytää riippumattomat komponentit estimoimalla matriisia, joka välittää edellä kuvatun lineaaritransformaation. Uusia näkökulmia riippumattomien komponenttien analyysiin esitetään kolmessa väitöskirjan artikkelissa. Yhdessä väitöskirja-artikkelissa esitetään uusi versio suositusta Deflation-based FastICA estimaattorista/algoritmista, jossa riippumattomat komponentit etsitään yksi kerrallaan. Tässä uudessa versiossa riippumattomat komponentit löydetään optimaalisessa järjestyksessä. Yhdessä artikkelissa esitetään (Le Cam mielessä) optimaalisia testaus - ja estimointimenetelmiä, kun riippumattomien komponenttien oletetaan tulevan symmetrisistä jakaumista. Yhdessä artikkelissa esitetään uusi menetelmä, jolla voidaan verrata erilaisia ICA estimaattoreita keskenään. Kaikissa kolmessa artikkelissa esitetään asymptoottisia tuloksia. Väitöskirjan viimeisessä luvussa uusia menetelmiä sovelletaan käytännön aineistoon.The aim of this doctoral thesis was to explore (asymptotical) characteristics of invariant coordinate system functionals and to introduce new approaches for independent component analysis. Equivariance and invariance issues arise in multivariate statistical analysis. Sometimes statistical procedures have to be modified to obtain an affine equivariant or invariant version. This can be done by preprocessing the data, e.g., by standardizing the multivariate data or by transforming the data to an invariant coordinate system. Two of the original articles deal with invariant coordinate selection and invariant coordinate system (ICS) functionals. Standardization of multivariate distributions, and characteristics of ICS functionals and statistics are examined. Also invariances up to some groups of transformations are discussed. Constructions of ICS functionals are addressed and asymptotical properties are explored. Also functionals and estimates of multivariate skewness and kurtosis are addressed. Application areas of ICS transformations are discussed. One important example of such application areas is independent component analysis. Independent component analysis is a very timely research area with a wide field of applications. In the independent component model the elements of a p-variate random vector are assumed to be linear combinations of the elements of an unobservable p-variate vector with mutually independent components. In the independent component analysis the aim is to recover the independent components by estimating an unmixing matrix that transforms the observed $p$-variate vector to the independent components. New approaches for independent component analysis are provided in three of the original articles. Deflation-based FastICA, where independent components are extracted one-by-one, is among the most popular methods for estimating an unmixing matrix in the independent component model. In the literature, it is often seen rather as an algorithm than an estimator related to a certain objective function, and only recently its statistical properties have been derived. One of the recent findings is that the order, in which the independent components are extracted in practice, has a strong effect on the performance of the estimator. A new reloaded procedure, to ensure that the independent components are extracted in an optimal order, is proposed in one of the articles. In one of the original articles, new optimal (in Le Cam sense) inference procedures are developed under symmetry assumption of the independent components. The inference procedures are based on signed ranks. Hypothesis tests, estimators and confidence regions are provided, and asymptotical properties are examined. The independent component model can be formulated in several ways: If the elements of a vector of independent components are permuted or multiplied by nonzero scalars, the vector still has independent components. The comparison of the performances of different unmixing matrix estimates is then difficult as the estimates are for different population quantities. A new natural performance index is suggested in one of the articles. The index is proven to possess several nice properties compared to previously presented indices, and it is easy and fast to compute. Also limiting behavior of the index, as the sample size approaches infinity, is explored. To demonstrate the use of the new methods in practise, a data example is provided in the last chapter of this thesis

Extensions of independent component analysis for natural image data

An understanding of the statistical properties of natural images is useful for any kind of processing to be performed on them. Natural image statistics are, however, in many ways as complex as the world which they depict. Fortunately, the dominant low-level statistics of images are sufficient for many different image processing goals. A lot of research has been devoted to second order statistics of natural images over the years. Independent component analysis is a statistical tool for analyzing higher than second order statistics of data sets. It attempts to describe the observed data as a linear combination of independent, latent sources. Despite its simplicity, it has provided valuable insights of many types of natural data. With natural image data, it gives a sparse basis useful for efficient description of the data. Connections between this description and early mammalian visual processing have been noticed. The main focus of this work is to extend the known results of applying independent component analysis on natural images. We explore different imaging techniques, develop algorithms for overcomplete cases, and study the dependencies between the components by using a model that finds a topographic ordering for the components as well as by conditioning the statistics of a component on the activity of another. An overview is provided of the associated problem field, and it is discussed how these relatively small results may eventually be a part of a more complete solution to the problem of vision.reviewe