%0 Journal Article
%T Dynamically Measuring Statistical Dependencies in Multivariate Financial Time Series Using Independent Component Analysis
%A Nauman Shah
%A Stephen J. Roberts
%J ISRN Signal Processing
%D 2013
%R 10.1155/2013/434832
%X We present a computationally tractable approach to dynamically measure statistical dependencies in multivariate non-Gaussian signals. The approach makes use of extensions of independent component analysis to calculate information coupling, as a proxy measure for mutual information, between multiple signals and can be used to estimate uncertainty associated with the information coupling measure in a straightforward way. We empirically validate relative accuracy of the information coupling measure using a set of synthetic data examples and showcase practical utility of using the measure when analysing multivariate financial time series. 1. Introduction The task of accurately inferring the statistical dependency structure (association) in multivariate systems has been an area of active research for many years, with a wide range of practical applications [1]. Many of these applications require real-time sequential analysis of dependencies in multivariate data streams with dynamically changing properties. However, most existing measures of dependence have some serious limitations; in terms of the type of data sets they are suitable for or in their computational complexities. If the data being analysed is generated using a known stable process, with known marginal and multivariate distributions, the degree of dependence can be estimated relatively easily. However, most real-world data sets have dynamically changing properties to which a single distribution cannot be assigned. Multivariate data generated in global financial markets is an example of such complex data sets. Financial data exhibits rapidly changing dynamics and is non-Gaussian in nature; this is especially true for financial data recorded at high frequencies [2]. In fact, as the scale over which financial returns are calculated decreases, their distribution becomes increasingly non-Gaussian, a feature referred to as aggregational Gaussianity. The recent explosive growth in availability and use of financial data sampled at high frequencies therefore requires the use of computationally efficient algorithms which are suitable for dynamically analysing dependencies in non-Gaussian data streams. The most commonly used measure of statistical dependence is linear correlation. However, practical use of the linear correlation measure has three main limitations; that is, it cannot accurately model dependencies between signals with non-Gaussian distributions [3]; it is restricted to measuring linear statistical dependencies and is very sensitive to outliers [4]. Rank correlation is another frequently used
%U http://www.hindawi.com/journals/isrn.signal.processing/2013/434832/