Statistics of heteroskedastic extremes
John H.J. Einmahl – Tilburg University, Laurens de Haan – Erasmus University Rotterdam and University of Lisbon
& Chen Zhou – De Nederlandsche Bank and Erasmus University Rotterdam

Do we have more frequent and severe financial crises nowadays than before? To answer such question, it is necessary to model the time variation of the tail region of the distribution of financial or economic indicators. This paper achieves this goal by extending classical extreme value theory to allow for non-identically distributed observations. When the distribution tails are proportional much of extreme value statistics remains valid. The proportionality function for the tails can be estimated nonparametrically, which displays the time variation in extremes. The proposed method can be applied to test whether conventional time invariant model is valid. More importantly, it can be applied to forecast high quantiles of distributions in the future.

Chen Zhou

Chen Zhou is an economist in Economics Policy and Research Division, De Nederlandsche Bank (The Dutch Central Bank). He is also an assistant professor in Rotterdam School of Management, Erasmus University Rotterdam. The general research topic of Chen Zhou is Extreme Value Theory and its applications in finance. Currently, he focuses on financial stability analysis, such as measuring systemic risk, identifying systemically important financial institutions and macroprudential regulations. Chen Zhou’s research on banking and finance has been published in various journals in finance such as Journal of Financial and Quantitative Analysis, Journal of Empirical Finance and International Journal of Central Banking. Besides, Chen Zhou’s research on statistics has been published in journals in statistics such as Journal of the Royal Statistical Society (Series B), Annals of Applied Statistics and Journal of Multivariate Analysis. To know more…


“Since I started working on extreme value analysis, most existing methods assume a time-invariant distribution for the underlying data. Little efforts have been devoted to time variation in the data generating process. However, in finance, due to financial innovation, such variation is inevitable. It is time to sink our teeth into this new field.”

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