Efficient Market Hypothesis, Stats

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. 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 countries. The alternate hypothesis is that the stock market returns are not weak form efficient. To be more specific, "not weak form efficient" means that the returns show a trend.

It is understood that by definition evidence of medium- or strong-form efficiency would also be evidence of weak-form efficiency, but it is worth clarifying this point to properly define the alternate hypothesis. A number of different statistical tests were undertaken in order to demonstrate the independence of market movements. These tests were the Augmented Dickey-Fuller (ADF), the Phillips-Peron (PP), VR, Wright ranks-and-signs test, serial correlation test, stationarity test and Hurst exponent analysis. The Augmented Dickey-Fuller (ADF) test will test the unit root to see if the time series is stationary.

A stationary time series implies that the mean and variance do not change in a predictable manner, which would mean that weak-form EMH holds. The Phillips-Peron (PP) test builds on the ADF test, using a slightly different methodology to test for independence within the data, again to support or reject the null hypothesis that developed and GCC markets demonstrate weak-form EMH. Variance ratio tests are also useful in testing the random walk hypothesis -- the VR, Chow-Denning VR and Wright's ranks-and-signs are all variance ratio tests.

The maximum absolute value of individual variance test ratio statistics can be used to reject the null hypothesis. Chow-Denning, for example, is used to test against large Type I errors in the standard variance ratio test (Chen, 2008). Wright's ranks-and-signs test introduces a different technique in order to test the data in a different way, in particular reducing the impact of size distortions on the data set, i.e. reducing the impact of massive daily market moves, thus reducing size distortions within the data series (Wright, 2000).

The serial correlation test is used to test for autocorrelation errors in the original regression model. Stationarity testing seeks to determine if the time series has constant mean, variance and autocovariance that does not change.