@Harrogath - I got this from one of the past posts. I did not understand - how past value is the best predictor of the value today when you cannot forecast a Random walk?
A random walk represents a random variable. Random means erratic, something with no predictable forecast. For example, exchange rates are best defined or modeled as random walks. So why E(e)=0 ?, because this means that the best forecast of X(t) is x(t-1). Sounds weird, but the explanation in simple words is that due you have no way to forecast a random walk, its past value is the best predictor of the value today (at t). So on average, E(e) should be zero.