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DISTANCE MEASURES, INCONSISTENCY MATRICES AND ALGORITHMS FOR THE STUDY OF EPIDEMIOLOGICAL AND FINANCIAL CRISES

Part of: Inference from stochastic processes Multivariate analysis

Published online by Cambridge University Press:  05 January 2022

NICK JAMES Open the ORCID record for NICK JAMES [Opens in a new window]
NICK JAMES*
Affiliation:
School of Mathematics and Statistics, University of Melbourne, Parkville, Victoria3010, Australia
*
e-mail: [email protected]
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Abstract

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Keywords

multivariate time seriesdistance measuresequitiesepidemiology

MSC classification

Primary: 62M10: Time series, auto-correlation, regression, etc.
Secondary: 62H12: Estimation 92D30: Epidemiology
Type
Abstracts of Australasian PhD Theses
Information
Bulletin of the Australian Mathematical Society , Volume 105 , Issue 2 , April 2022 , pp. 349 - 350
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Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.

This thesis introduces several new methods for multivariate time series analysis and then applies these methods to understand the behaviour of financial crises and the Covid-19 pandemic. In particular, we introduce a new semi-metric between finite sets and use it to measure distance in various settings, including between the sets of change points and turning points of time series. We also develop a new algorithmic framework to detect such change points subject to flexible parameters.

Rather than studying financial securities on an individual basis, we introduce new algorithmic frameworks to study the collective dynamics of entire asset classes and determine how these dynamics change over time. The algorithmic frameworks and distances between time series have potential applications beyond this thesis. We perform detailed analyses on equities, cryptocurrencies and international financial indices, comparing their behaviour in a range of experiments. We demonstrate substantially more homogeneity within the cryptocurrency market than the equity market, and show substantial homogeneity between the equity indices of countries during the Covid-19 pandemic.

We also study the human cost of the pandemic closely, particularly regarding the multivariate time series of cases and deaths on a country-by-country basis around the world and on a state-by-state basis in the United States. We develop several methods to determine the most suitable offset between cases and deaths, both on a country-by-country and worldwide basis. We develop methods that identify the most anomalous countries with respect to the progression of cases to deaths, classify countries and US states according to their differing wave behaviour of the disease, and reveal substantial reductions in mortality in subsequent surges. Such analysis may help European countries and US states alike to learn from each other’s experiences and differing successes to develop the best policies to combat Covid-19 as a collective unit.

The thesis is based on seven published papers [Reference James1–Reference James, Menzies and Radchenko7].

Footnotes

Thesis submitted to the University of Sydney in April 2021, degree approved on 9 July 2021, supervisor Jennifer Chan.

References

James, N., ‘Dynamics, behaviours, and anomaly persistence in cryptocurrencies and equities surrounding COVID-19’, Phys. A 570 (2021), Article ID 125831.10.1016/j.physa.2021.125831CrossRefGoogle Scholar
James, N. and Menzies, M., ‘Cluster-based dual evolution for multivariate time series: analyzing COVID-19’, Chaos 30 (2020), Article ID 061108.10.1063/5.0013156CrossRefGoogle Scholar
James, N. and Menzies, M., ‘COVID-19 in the United States: trajectories and second surge behavior’, Chaos 30 (2020), Article ID 091102.10.1063/5.0024204CrossRefGoogle ScholarPubMed
James, N. and Menzies, M., ‘Association between COVID-19 cases and international equity indices’, Phys. D 417 (2021), Article ID 132809.10.1016/j.physd.2020.132809CrossRefGoogle ScholarPubMed
James, N., Menzies, M., Azizi, L. and Chan, J., ‘Novel semi-metrics for multivariate change point analysis and anomaly detection’, Phys. D 412 (2020), Article ID 132636.10.1016/j.physd.2020.132636CrossRefGoogle ScholarPubMed
James, N., Menzies, M. and Chan, J., ‘Changes to the extreme and erratic behaviour of cryptocurrencies during COVID-19’, Phys. A 565 (2021), Article ID 125581.10.1016/j.physa.2020.125581CrossRefGoogle Scholar
James, N., Menzies, M. and Radchenko, P., ‘COVID-19 second wave mortality in Europe and the United States’, Chaos 31 (2021), Article ID 031105.10.1063/5.0041569CrossRefGoogle ScholarPubMed