of weak-form efficiency is that investors cannot predict future trends by extrapolating past
events. At an empirical level, this implies that the market follows a ‘random walk’ as only an
unknown event may modify prices instantaneously. The latter property being straightforward
to formalize, market efficiency is often defined based on time series econometrics. More
precisely, efficient prices may be characterized by the following process (Barhoumi, 2005):
Pt = Pt-1 +εt (1)
Where Pt is the asset price at time t, Pt-1 is the asset price at time t-1 and εt is a randomly
distributed variable with 0 mean and variance tσ2. Assuming the absence of serial
autocorrelation, we have:
E [Pt+1 / (..., P-1. P )] = E [Pt + ε,+1 / (..., P-1, P )]
E [P,+1 / (..., P-1, P )] = E [P /(.... Pt-1, P )]+ E [s, +1 / (..., P-1, P )] (2)
E[P,+1/(...,P,-1,P,)]=E[P,/(...,P,-1,P,)]
According to (2), current prices constitute an appropriate expectation for the price in t+1.
Besides, the variance of expected prices is given by:
V [P,+1/ (..., P,-1, P, )]= V [Pt + ε,+1/(..., P,-1, P, )]
V[Pt+1/(...,Pt-1,Pt)]=0+V(εt+1) (3)
V[Pt+1 /(...,Pt-1,Pt)]= V(εt)
As shown in (3), the variance of the expected price is equal to the variance of the random
variableεt . As a result, only the variance of the error term can explain the time-varying
pattern of asset prices, whose changes do not help predicting future values. Hence, the