IDEAS home Printed from
   My bibliography  Save this paper

Does the Compass Rose pattern matter for testing normality?


  • ANNAERT, Jan
  • CLAES, Anouk G.P.
  • DE CEUSTER, Marc J.K.


Some years ago, Crack and Ledoit (1996) discovered a strikingly geometric structure when plotting US stock returns against themselves. Since this pattern, in which lines radiating from the origin pop up, resembles the navigating tool it was named “Compass Rose”. Although authors differ in opinion when explaining the causes of the phenomenon, discreteness of price jumps is unanimously indicated as driver of the structure. This paper first documents the presence of a Compass Rose Structure within the illiquid Belgian stock market, looking at both individual stocks and stock indices. We then examine whether the presence of a Compass Rose, i.e. the discreteness of prices, affects normality tests. Based on simulated Brownian Motions with rounded price increments, we notice that two commonly used normality tests react differently to discreteness in the underlying data. As the tick size increases, the popular Jarque-Bera test is not able to detect the deviations from normality. The Lilliefors test, however, clearly rejects the normality assumption when the data exhibit tick/volatility ratios in excess of 2.5.

Suggested Citation

  • ANNAERT, Jan & CLAES, Anouk G.P. & DE CEUSTER, Marc J.K., 2003. "Does the Compass Rose pattern matter for testing normality?," Working Papers 2003020, University of Antwerp, Faculty of Applied Economics.
  • Handle: RePEc:ant:wpaper:2003020

    Download full text from publisher

    File URL:
    Download Restriction: no

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:


    Access and download statistics


    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:ant:wpaper:2003020. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Joeri Nys). General contact details of provider: .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.