Real time clustering of time series using triangular potentials

TL;DR

This paper introduces a real-time clustering method for time series using triangular potentials, aiming to improve investment portfolio construction by grouping assets with similar return characteristics without relying on covariance matrix inversion.

Contribution

It proposes a novel clustering technique based on triangular potentials, providing theoretical insights and demonstrating its effectiveness with synthetic data examples.

Findings

The method effectively clusters assets with similar return patterns.

It avoids covariance matrix inversion, reducing estimation errors.

Theoretical results support the clustering approach.

Abstract

Motivated by the problem of computing investment portfolio weightings we investigate various methods of clustering as alternatives to traditional mean-variance approaches. Such methods can have significant benefits from a practical point of view since they remove the need to invert a sample covariance matrix, which can suffer from estimation error and will almost certainly be non-stationary. The general idea is to find groups of assets which share similar return characteristics over time and treat each group as a single composite asset. We then apply inverse volatility weightings to these new composite assets. In the course of our investigation we devise a method of clustering based on triangular potentials and we present associated theoretical results as well as various examples based on synthetic data.