Size and power properties of tests of the martingale difference hypothesis: a Monte Carlo study

This paper compares the performance of a wide range of approaches to testing the martingale difference hypothesis in economic and financial time series. An extensive Monte Carlo experiment is conducted to evaluate and compare the alternative tests under a martingale difference null hypothesis, which allows for conditional heteroskedasticity and a fat tailed marginal distribution, against alternative hypotheses which receive empirical support in the financial markets. It is found that the wild bootstrap (WB) test, Chow and Denning's variant of a sign test with zero drift, CD<SUB align="right">(S1)</SUB>, and the bootstrap adjusted sign tests, BS<SUB align="right">(S1) </SUB> and BS<SUB align="right">(S2)</SUB>, are superior to others in that they show desirable size properties under the martingale difference null and excellent power properties against a variety of non-martingale alternatives. In addition, they are all non-parametric finite sample tests and so do not rely on large sample theories for statistical inference: indeed, the BS<SUB align="right">(S2)</SUB> test requires no strong assumptions on the distribution of the time series being tested.