I am trying to use both ADF test and variance ratio test for random walk. However, the ADF test tells me my financial time series contains unit root, but variance ratio test (lo-mackinlay) rejected that financial time series is random walk (Raito 0.86) at lag 2, but insiganificant at all other meaningful lags. Now my questions are follow:
1, Did I make a mistake by thinking that unit root entails random walk, thus two tests do not conflict each other.
2, If I am correct in thinking that unit root does entails random walk, then the ADF and Variance ratio test tells different story. How can that occur.
3, Also, for robustness check, I did KPSS test and it rejected null hypothesis in favour of alternative, intails the financial time series contain unit roots.