Testing the white noise hypothesis of stock returns

Weak form efficiency of stock markets implies unpredictability of stock returns in a time series sense, and the latter is tested predominantly under a serial independence or martingale difference assumption. Since these properties rule out weak dependence that may exist in stock returns, it is of interest to test whether returns are white noise. We perform white noise tests assisted by Shao's (2011) blockwise wild bootstrap. We reveal that, in rolling windows, the block structure inscribes an artificial periodicity in bootstrapped confidence bands. We eliminate the periodicity by randomizing a block size. The white noise hypothesis is accepted for Chinese and Japanese markets, suggesting that those markets are weak form efficient. The white noise hypothesis is rejected for U.K. and U.S. markets during the Iraq War and the subprime mortgage crisis due to significantly negative autocorrelations, suggesting that those markets are inefficient in crisis periods.