"When performing a variance ratio test on stock index prices, a variance ratio significantly >1 indicates that stock index prices follow a random walk" True or False?Variance-Ratio test is a measure of the randomness of a return series. Variance ratio is computed by dividing the variance of returns estimated from longer intervals by the variance of returns estimated from shorter intervals, (for the same measurement period), and then normalizing this value to one by dividing it by the ratio of the longer interval to the shorter interval. A variance ratio that is greater than one suggests that the returns series is positively serially correlated or that the shorter interval returns trend within the duration of the longer interval. A variance ratio that is less than one suggests that the return series is negatively serially correlated or that the shorter interval returns tend toward mean reversion within the duration of the longer intervalRandom Walk - Is the financial theory that asserts that changes in price or rate time series are unpredictable. However, the theory recognizes that there is a statistical interdependency between the data. This non-random stickiness is sometimes referred to as autocorrelation or serial correlation.So the statement is true right?

first of all the variance ratio tests that i am aware of are applied to log returns instead of prices because they work well only when the underlying distribution is assumed to be normal. Now i believe that if the ratio you have described is close to 1, this indicates that there is a random walk in which case the statement is wrong. and this is what one should expect because if there is a random walk then the variances at the larger horizon is just the sum of variances at the shorter horizon and hence when you calculate the ratio and normalize, the ratio should be 1.now if the ratio is significantly > 1, then what it means is that you cannot neglect the covariances in the short term and that these covariances are +ve implying that if the underlying assumption is normal, then there exists positive serial correlations. similarly we can argue for ratio significantly < 1. the last statement that you have made about a random walk, where have you got it ? and have you researched the reasons ? i mean the statistical dependence could be due to a false assumtption of normality or it could be due to lack of data or it could be due to outliers or due to lack of an efficient and unbiased estimator, so please be more specific as to the origins of the last statement.