Motivated by the risk inherent in intraday investing, we propose several ways of quantifying extremal behavior of a time series of curves. A curve can be extreme if it has shape and/or magnitude much different than the bulk of observed curves. Our approach is at the nexus of functional data analysis and extreme value theory. The risk measures we propose allow us to assess probabilities of observing extreme curves not seen in a historical record. These measures complement risk measures based on point-to-point returns, but have different interpretation and information content. Using our approach, we study how the financial crisis of 2008 impacted the extreme behavior of intraday cumulative return curves. We discover different impacts on shares in important sectors of the US economy. The information our analysis provides is in some cases different from the conclusions based on the extreme value analysis of daily closing price returns.
Brooks, C., A. D. Clare, J. W. Dalle Molle, and G. Persand. 2005. “A Comparison of Extreme Value Theory Approaches for Determining Value-at-Risk.” Journal of Empirical Finance 12: 339–52.10.1016/j.jempfin.2004.01.004)| false
Dionne, G., P. Duchesne, and M. Pacurar. 2009. “Intraday Value at Risk (ivar) using Tick-by-tick Data with Application to the Toronto Stock Exchange.” Journal of Empirical Finance 16: 777–92.10.1016/j.jempfin.2009.05.005)| false
Gençay, R., and F. Selçuk. 2004. “Extreme Value Theory and Value-at-Risk: Relative Performance in Emerging Markets.” International Journal of Forecasting 20: 287–303.10.1016/j.ijforecast.2003.09.005)| false
McNeil, A. J., and R. Frey. 2000. “Estimation of Tail-Related Risk Measures for Het- Eroscedastic Financial Time Series: An Extreme Value Approach.” Journal of Empirical Finance 7: 271–300.10.1016/S0927-5398(00)00012-8)| false
Poon, S., M. Rockinger, and J. Tawn. 2004. “Extreme Value Dependence in Financial Markets: Diagnostics, Models, and Financial Implications.” The Review of Financial Studies 17: 581–610.10.1093/rfs/hhg058)| false
The Journal of Time Series Econometrics (JTSE) serves as an internationally recognized outlet for important new research in both theoretical and applied classical and Bayesian time series, spatial and panel data econometrics. The scope of the journal includes papers dealing with estimation, testing and other methodological aspects involved in the application of time series and spatial analytic techniques to economic, financial and related data.