Monitoring the Intraday Volatility Pattern

  • 1 Department of Information and Operations Management, Marshall School of Business, University of Southern California, Los Angeles, CA, USA
  • 2 Department of Mathematics, Université Libre de Bruxelles, CP 210 Bd. du Triomphe, Brussels 1050, Belgium
  • 3 Department of Statistics, Colorado State University, Fort Collins, CO, USA
Robertas Gabrys, Siegfried Hörmann and Piotr Kokoszka

Abstract

A functional time series consists of curves, typically one curve per day. The most important parameter of such a series is the mean curve. We propose two methods of detecting a change in the mean function of a functional time series. The change is detected on line, as new functional observations arrive. The general methodology is motivated by, and applied to, the detection of a change in the mean intraday volatility pattern. The methodology is asymptotically justified by applying a new notion of weak dependence for functional time series. It is calibrated and validated by simulations based on real intraday volatility curves.

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