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This paper presents first steps towards robust models for crisis prediction. We conduct a horse race of conventional statistical methods and more recent machine learning methods as early-warning models. As individual models are in the literature most often built in isolation of other methods, the exercise is of high relevance for assessing the relative performance of a wide variety of methods. Further, we test various ensemble approaches to aggregating the information products of the built models, providing more robust basis for measuring country-level vulnerabilities. Finally, we provide approaches to estimating model uncertainty in early-warning exercises, particularly model performance uncertainty and model output uncertainty. The approaches put forward in this paper are shown with Europe as a playground. Generally, our results show that the conventional statistical approaches are outperformed by more advanced machine learning methods, such as k-nearest neighbours and neural networks, and particularly by model aggregation approaches through ensemble learning.
Acknowledgements
We are grateful to Johannes Beutel, Andras Fulop, Benjamin Klaus, Jan-Hannes Lang, Tuomas A. Peltonen, Roberto Savona, Gregor von Schweinitz, Eero Tölö, Peter Welz and Marika Vezzoli for useful comments on previous versions of the paper. The paper has also benefited from comments during presentations at BITA’14 Seminar on Current Topics in Business, IT and Analytics in Helsinki on 13 October 2014, seminars at the Financial Stability Surveillance Division at the ECB in Frankfurt am Main on 21 November 2014 and 12 January 2015, a seminar at the Bank of Finland in Helsinki on 28 November 2014, the 1st Conference on Recent Developments in Financial Econometrics and Applications at Deakin University in Geelong on 4–5 December 2014, the XXXVII Annual Meeting of the Finnish Economic Association in Helsinki on 12 February 2015, 8th Financial Risks International Forum on Scenarios, Stress and Forecasts in Finance in Paris on 30–31 March 2015, seminar at the European Commission Joint-Research Centre in Ispra on 13 April 2015, seminar at the University of Brescia on 14 April 2015, Financial Stability seminar at the Deutsche Bundesbank in Frankfurt am Main on 21 May 2015, the SYRTO conference ’A Critical Evaluation of Econometric Measures for Systemic Risk’ in Amsterdam on 5 June 2015, the INFINITI conference in Ljubljana, Slovenia on 9 June 2015, Financial Stability seminar at the Bank of Estonia on 30 June 2015, seminar at University of Pavia on 3 September 2015, keynote at the 5th CCCS Student Science Fair at University of Basel on 16 September 2015, seminar at Aalto University in Helsinki on 11 January 2016, seminar at University of Basel on 4 April 2016, seminar at ETH Zurich on 3 August 2016, seminar at Riksbanken in Stockholm on 10 November 2016, and seminar at University of Oxford on 10 May 2017. The horse race in this paper is an implementation of a proposal for a Lamfalussy Fellowship in 2012. Several of the methods and exercises presented in this paper have also been implemented in an online platform for interactive modelling (produced in conjunction with and is property of infolytika): http://cm.infolytika.com. For further information see Holopainen and Sarlin (2015). The second author thanks the GRI in Financial Services and the Louis Bachelier Institute for financial support. All errors are our own.