Efficient Market Hypothesis, Stats Hypothesis Chapter

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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 in question.

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A rejection of the null hypothesis would imply that weak form EMH does hold in the asset or market in question.

Methodology

To determine weak form EMH in developed and GCC countries, a series of tests can be applied. First, if EMH holds, then that implies that the markets move in a random walk, which means that the movements from one day to the next are not trend-bound and therefore cannot be predicted. The tests will therefore focus on establishing the conditions for the random walk.

Ho = GCC stock market returns are normally distributed

Establishing whether or not returns on normally distributed is the first step in this type of analysis because the statistical tests that will be applied at later stages will differ depending on whether or not the market returns are normally distributed. The null hypothesis is therefore that the GCC market returns are normally distributed, because that would support the other tests conducted, and would reflect random walk conditions (Jamaani & Roca, 2015). The alternate hypothesis is that the returns are not normally distributed.

Ho = Developed and GCC stock market returns are weak form efficient.

This null hypothesis is measured using a number of different tests that will examine the degree of independence between market movements in both GCC and developed….....

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