AStA Advances in Statistical Analysis

, Volume 91, Issue 1, pp 3–21 | Cite as

A Hausman test for Brownian motion

  • Martin Becker
  • Ralph Friedmann
  • Stefan Klößner
  • Walter Sanddorf-Köhle
Original Paper


New tests are proposed for the specification of the intraday price process of a risky asset, based on open, high, low, and close prices. Under the null of a Brownian process we derive two stochastically independent, unbiased volatility estimators. For a Hausman specification test we prove its equivalence with an F-test, consider its robustness against variation in drift and volatility, and analyze the power against an Ornstein–Uhlenbeck process, as well as a random walk with alternative distributions.


Hausman test Brownian process High-Low-Prices 


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Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  • Martin Becker
    • 1
  • Ralph Friedmann
    • 1
  • Stefan Klößner
    • 1
  • Walter Sanddorf-Köhle
    • 1
  1. 1.Lehrstuhl für Statistik und ÖkonometrieUniversität des SaarlandesSaarbrückenGermany

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