The main objective of this thesis is to show that additional insights, beyond the verdict of market efficiency/inefficiency, can be obtained from those existing statistical tests of the weak-form efficient markets hypothesis (EMH). As an introduction, Chapter 1 provides the background and outline of this thesis. Chapter 2 then surveys the relevant literature and discusses the motivations behind the development of the three key research questions addressed in Chapter 3 through 5, respectively. Chapter 3 examines the association between trade liberalization and the weak-form efficiency of stock market, motivated by the production-based asset pricing model of Basu and Morey [Trade opening and the behavior of emerging stock market prices, Journal of Economic Integration 20(1), 2005, 68-92]. Using data from 23 developing countries over the sample period of 1992-2006, we find that a greater level of de facto trade openness is associated with a higher degree of informational efficiency in these emerging stock markets, even after controlling for trading volume and market return volatility. Further analyses find no significant association between the extent of financial openness and the degree of informational efficiency. While Chapter 3 provides novel evidence on the association between trade openness and stock market efficiency, our empirical work can also be viewed as addressing the issue of whether the existing theoretical determinants (i.e. trading volume, return volatility, trade liberalization and financial openness) are capable of explaining the variations of index return autocorrelations across countries and over time. Chapter 4 employs the rolling bicorrelation test to measure the degree of nonlinear departures from a random walk for aggregate stock price indices of 50 countries over the common sample period of 1995-2005. We find that stock markets in economies with low per capita GDP in general experience more frequent price deviations than those in the high incom.