A number of statistical tests comprising Ljung-Box Q statistics test, Runs test, GARCH volatility test and variance ratio test have been used to test randomness of world markets.

The variance ratio test developed by Lo and MacKinlay (1988), which was considered to be a powerful tool in detecting departures from randomness (Taylor, 2005; Dias et al.

Using the

variance ratio test, he pointed out that the random model on weekly returns did exist for those countries.

The results of unit root test accepted the null hypothesis of random walk for all the indices, whereas it was rejected using corrected

variance ratio test.

Using the Cochrane (1988)

variance ratio test and the Campbell and Mankiw (1987) variance decomposition test, they suggest that the real net discount ratio follows a trend stationary process with mean-reverting properties.

To separate the random component from the systematic component reflecting the changes of an underlying economic model, we employ the

variance ratio test first developed by Tintner (1940) and the corresponding tests statistics by Lo and MacKinlay (1988).

MacKinlay, 1989, "The Size and Power of the

Variance Ratio Test in Finite Samples: A Monte Carlo Investigation," Journal of Econometrics 40, 203-238.

If this "planned" addition to inventory is large enough, the

variance ratio test for smoothing will fail.

Evidence of Weak Level Efficiency - Introduction; Serial Correlation Coefficient Test; Runs Test;

Variance Ratio Test.

We implement the

variance ratio test for k = 5 trading days.

The purpose of applying the Cochrane

variance ratio test and Campbell-Mankiw decomposition test is to estimate the size of the random walk or permanent stochastic trend component in the net discount ratio.

Of the 177 stocks, 145 exhibit negative autocorrelation by runs ratio tests and 140-exhibit negative autocorrelation by

variance ratio tests.