Roll arithmetic

From one day of trade prices in an NSE stock you compute $\widehat{\operatorname{Var}}(\Delta p) = 0.0050$ ₹² and $\hat\gamma_1 = -0.0016$ ₹². (a) Estimate the spread and the variance of efficient-price changes per trade. (b) What is the first-order autocorrelation of trade-price changes? (c) On daily closing prices of the same stock you find $\hat\gamma_1 > 0$. What does this mean for the estimator, and what would you do instead?