2016/03/25 by Gautier Marti, Frank Nielsen, Marti, Gautier +5
Computer Science · Economics, Econometrics and Finance · #Complex Systems and Time Series Analysis #FOS: Computer and information sciences #FOS: Economics and business #Methodology (stat.ME) #Statistical Finance (q-fin.ST) #Time Series Analysis and Forecasting
paper · pdf · doi:10.48550/arxiv.1603.07822
openalex publication_date 2016/03/25 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28
The following working document summarizes our work on the clustering of\nfinancial time series. It was written for a workshop on information geometry\nand its application for image and signal processing. This workshop brought\nseveral experts in pure and applied mathematics together with applied\nresearchers from medical imaging, radar signal processing and finance. The\nauthors belong to the latter group. This document was written as a long\nintroduction to further development of geometric tools in financial\napplications such as risk or portfolio analysis. Indeed, risk and portfolio\nanalysis essentially rely on covariance matrices. Besides that the Gaussian\nassumption is known to be inaccurate, covariance matrices are difficult to\nestimate from empirical data. To filter noise from the empirical estimate,\nMantegna proposed using hierarchical clustering. In this work, we first show\nthat this procedure is statistically consistent. Then, we propose to use\nclustering with a much broader application than the filtering of empirical\ncovariance matrices from the estimate correlation coefficients. To be able to\ndo that, we need to obtain distances between the financial time series that\nincorporate all the available information in these cross-dependent random\nprocesses.\n