This study utilizes the windowed-test procedure of Hinich and Patterson (1995) to examine the data generating process of KLCI returns series. Our econometrics results indicate that linear and non-linear dependencies play a significant role in the underlying dynamics of the returns series, implying the potential of returns predictability. However, these dependency structures are not stable and persistent across time as the results reveal their episodic and transient behaviour, and hence do not bring much benefit to investors. Moreover, for most of the time periods, the returns series move along at a close approximation to random walk. As a whole, the results do not constitute strong evidence against the weak-form EMH in Bursa Malaysia. More importantly, the instability of the underlying data generating process makes it difficult to model the behaviour of the returns series over long time histories, rendering long-horizons prediction difficult if not impossible.