The correct answer is A. independent of each other.
The weak form of the efficient-market hypothesis (EMH) states that past prices cannot be used to predict future prices. In other words, the current price of a security reflects all available information, including past prices.
If successive price changes over time are independent of each other, then it is impossible to predict future prices based on past prices. This is because each price change is determined by new information that is not correlated with past information.
Options B, C, and D are incorrect because they would all suggest that past prices can be used to predict future prices. For example, if successive price changes are negative, then this would suggest that the price of the security is likely to continue to decline in the future. However, the weak form of the EMH states that this is not possible.
In conclusion, the weak form of the EMH is supported if successive price changes over time are independent of each other. This means that past prices cannot be used to predict future prices.