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Sankhya A

, Volume 76, Issue 2, pp 219–256 | Cite as

Robust Surveillance of Covariance Matrices Using a Single Observation

  • Olha Bodnar
  • Taras Bodnar
  • Yarema OkhrinEmail author
Article

Abstract

In this paper a new technique for monitoring shifts in covariance matrices of Gaussian processes is developed. The processes we monitor are obtained from the covariance matrices estimated using a single observation. These processes follow independent Gaussian distribution in the in-control state, thus allowing for application of standard control charts. Furthermore, in contrary to the existing literature, the suggested procedure is asymptotically robust to the shifts in the mean. The explicit out-of-control distribution for an arbitrary moment of the shift is derived. The performance of numerous multivariate control charts is evaluated in an extensive simulation study and applied to monitoring volatilities on financial markets.

Keywords and phrases

singular Wishart distribution CUSUM EWMA skew-normal distribution expected delay 

AMS (2000) subject classification

Primary 62L10 Secondary 62H10 

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Copyright information

© Indian Statistical Institute 2013

Authors and Affiliations

  1. 1.Physikalisch-Technische BundesanstaltBerlinGermany
  2. 2.Department of MathematicsHumboldt-University of BerlinBerlinGermany
  3. 3.Department of StatisticsUniversity of AugsburgAugsburgGermany

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