CFDP 1912

Testing the Martingale Hypothesis

Author(s): 
Peter C. B. PhillipsSainan Jin

Publication Date: September 2013

Pages: 46

Abstract: 

We propose new tests of the martingale hypothesis based on generalized versions of the Kolmogorov-Smirnov and Cramér-von Mises tests. The tests are distribution free and allow for a weak drift in the null model. The methods do not require either smoothing parameters or bootstrap resampling for their implementation and so are well suited to practical work. The paper develops limit theory for the tests under the null and shows that the tests are consistent against a wide class of nonlinear, non-martingale processes. Simulations show that the tests have good finite sample properties in comparison with other tests particularly under conditional heteroskedasticity and mildly explosive alternatives. An empirical application to major exchange rate data finds strong evidence in favor of the martingale hypothesis, confirming much earlier research.

Keywords: 

Brownian functional, Martingale hypothesis, Kolmogorov-Smirnov test, Cramér-von Mises test, Explosive process, Exchange rates

JEL Classification Codes: C12

See CFP: 1443