Consider the tick-by-tick transactions data of the stock of Starbucks from July 25 to July 29, 2011. The data are in taq-sbux-jul2011.txt. Focus on trades occurred in the normal trading hours.

(a) Obtain the intraday 5-min log returns of the stock. Plot the histogram of the returns.

(b) Obtain daily realized volatility of the stock using 5-min intraday \(\log\) returns.

(c) Obtain daily realized volatility of the stock using 1-min intraday log returns using subsampling method with the average estimator.

(d) Obtain daily realized volatility of the stock using 1-min intraday log returns using subsampling method with the two-scale estimator.