Random-walk model of prices

A simple model writes the next price as the current price plus a drift term and a new random innovation. Independence or lack of predictability concerns the innovations or changes, not the successive price levels. A positive drift can make expected changes positive without making the next actual movement predictable. Equal probabilities of an increase and decrease are not required by every random-walk specification. Distinguish this statistical model from the broader weak-form efficiency proposition about abnormal returns after risk and costs; one is not an automatic empirical proof of the other.