Estimation of Cointegration Vectors in Time Series via Global Optimisation

TL;DR

This paper introduces a novel optimization-based approach for estimating cointegration vectors in time series, leveraging techniques from Independent Component Analysis to improve performance especially with limited data samples.

Contribution

It presents two new cointegration testing methods inspired by ICA, offering computational simplicity and better performance in small samples compared to traditional tests.

Findings

Methods outperform Johansen's test in limited sample scenarios

Decorrelation and nongaussianity maximization effectively detect cointegration

Approach is computationally efficient and accessible for practitioners

Abstract

Time Series Analysis has been given a great amount of study in which many useful tests were developed. The phenomenal work of Engle and Granger in 1987 and Johansen in 1988 has paved the way for the most commonly used cointegration tests so far. Even though cointegrating relationships focus on long-term behaviour and correlation of multiple nonstationary time series, oftentimes we encounter statistical data with limited sample sizes and other information. Thus other tests with empirical advantages may also be of considerable importance. In this paper, we provide an optimisation approach motivated by the Blind Source Separation, or also known as Independent Component Analysis, for cointegration between financial time series. Two methods for cointegration tests are introduced, namely decorrelation for the bivariate case and maximisation of nongaussianity for higher-dimensions. We highlight the empirical preponderances of independent components and also the computational simplicity, compared to common practices of cointegration such as the Johansen's Cointegration Test. The advantages of our methods, especially the better performances in limited sample size, enable a wider range of application and accessibility for researchers and practitioners to identify cointegrating relationships.