Data-Driven Smooth Tests for the Martingale Difference Hypothesis Articles uri icon

publication date

  • August 2010

start page

  • 1983

end page

  • 1998


  • 8


  • 54

International Standard Serial Number (ISSN)

  • 0167-9473

Electronic International Standard Serial Number (EISSN)

  • 1872-7352


  • A general method for testing the martingale difference hypothesis is proposed. The new tests are data-driven smooth tests based on the principal components of certain marked empirical processes that are
    asymptotically distribution-free, with critical values that are already
    tabulated. The data-driven smooth tests are optimal in a semiparametric
    sense discussed in the paper, and they are robust to conditional
    heteroskedasticity of unknown form. A simulation study shows that the
    smooth tests perform very well for a wide range of realistic
    alternatives and have more power than the omnibus and other competing
    tests. Finally, an application to the S&P 500 stock index and some
    of its components highlights the merits of our approach.