In relation to traded asset prices, a situation in which the price change in successive time periods is uncorrelated with previous time periods. In other words, the correlation coefficient between successive periods' price movements is zero.
(i) Future price changes cannot be predicted from the historical price record.
(ii) Assuming constant volatility in all relevant periods, the relevant measure of the standard deviation of the market price increases with the square root of the relative time period. For example the 9-month standard deviation would be expected to be three times ( = square root of 9) times as great as the one-month standard deviation.
A similar pattern of change over time in any other data series.