Dynamically Measuring Statistical Dependencies in Multivariate Financial Time Series Using Independent Component Analysis

Nauman Shah,Stephen Roberts

doi:10.1155/2013/434832

Abstract

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.

Highlights

The task of accurately inferring the statistical dependency structure in multivariate systems has been an area of active research for many years, with a wide range of practical applications [1]
We present a computationally efficient independent component analysis (ICA) based approach to dynamically measure information coupling in multivariate non-Gaussian data streams as a proxy measure for mutual information
The following notations are used for different measures of statistical dependence in this paper: ICA-based information coupling (η), linear correlation (ρ), rank correlation, and normalised mutual information (IN)

Summary

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. Multivariate data generated in global financial markets is an example of such complex data sets. The recent explosive growth in availability and use of financial data sampled at high frequencies requires the use of computationally efficient algorithms which are suitable for dynamically analysing dependencies in non-Gaussian data streams

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