Efficient Market Hypothesis
As previously discussed, the weak form efficiency suggests that share prices should follow a random walk, in that each change in share price is unpredictable based on past information. Formally, this is expressed in the following relationship:
where the variables are independent and identically distributed random variables representing equity prices at times 1,2,3…,k. So X is the equity price, the equity price at a point in time n and the change in equity price at any given time is not explained by the past equity price.
The augmented Dickey-Fuller test considers the following model:
where p is the lag order of the process which can be determined by the examination of autocorrelation and autocorrelation plots, and are the factors determined by the regression. The unit root test has the null hypothesis, and the rejection of the null hypothesis implies that the time series is stationary. The variable y refers to the unit root; when if the unit root changes over time in a predictable manner, then y=1, which implies a stationary process. If this is a stationary process, then the mean and variance do not change in a predictable manner.
Thus, if the null hypothesis holds, then the process is non-stationary, meaning that the mean and variance will change over time, following a trend. Those conditions, if they hold, mean that weak form EMH does not hold for the asset or market...
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