Is there autocorrelation in stock prices?
Stock prices follow a random walk process, usually we include a drift term to account for the somewhat prolonged upward/downward drifts. This is basically an AR(p) process, p being the lag order. For instance AR(1) with drift is $X_t=\delta+\beta X_{t-1}+u_t$ where $\beta = 1$. Try testing this model for unit root using ADF test in stata. One lag is enough. You should fail to reject the unit root for an evidence of autocorrelation in the prices. Stock returns are not autocorrelated, they usually follow a stationary process if you take sufficiently long sample.