What is a key characteristic of a Martingale process?

A key characteristic of a Martingale process is that it describes a random process where the future value is not predictable based on past values. Specifically, in a Martingale, the conditional expectation of the next value given all past values is equal to the current value. This indicates that there is no inherent trend or predictable pattern, making future values inherently unpredictable. In financial terms, a Martingale model suggests that the expected future price of a security, given the present price and all available information, is equal to the present price. This aligns directly with the concept that the future values are unpredictable, bolstering the idea that price movements are random, reflecting the efficient market hypothesis where past price movements do not provide useful information for predicting future prices.