Testing the martingale difference hypothesis in the UK stock and foreign exchange markets

This dissertation is concerned with testing the martingale difference hypothesis (MDH) in the returns of the UK stock indices and foreign exchange rates. The investigation has been carried on from two aspects. First, a wide range of approaches concerning testing the MDH in economic and financial time series are briefly reviewed. An extensive Monte Carlo experiment is conducted to evaluate and compare the performances of the alternative tests. It is found that the wild bootstrap (WB) test, the Chow and Denning’s test based on sign test with zero drift, CD(S₁), and the bootstrap adjusted sign tests, BS(S₁) and BS(S₂), are superior to others by showing desirable size properties under the martingale difference sequence and excellent power properties against a variety of nonmartingale alternatives. In addition, they are all non-parametric finite sample tests and do not rely on large sample theories for statistical inferences, of which the BS(S₂) even require no strong assumptions on the distribution of asset returns. Second, the statistics of drawdowns, which measure the successive losses over elastic time scale, can detect the subtle dependences in the very large successive price variations. Therefore, they are applied to test the MDH in this study following Somette (2004). If the successive price variations are not correlated, the drawdowns will distribute as stretched exponentials, or equivalently, any deviations from this distribution will suggest the existence of dependences in the returns.

All the MDH tests are applied to the empirical data of four major FTSE stock indices and exchange rates of four major currencies against the British pound. The results of best-performing conventional tests suggest that the MDH is rejected for three of eight return series, whereas the statistics of drawdowns detect the dependences in large successive returns for most time series except for the €/£ exchange rates, which have short-history data available. In view of the advantages and limitations of each testing method, it is concluded that the returns of all examined series are dependent, especially during the financial market crashes.