The file mmm9912-dtp. txt contains the transactions data of the stock of \(3 \mathrm{M}\) Company in December 1999. There are three columns: day of the month, time of transaction in seconds from midnight, and transaction price. Transactions that occurred after 4:00 Pм Eastern time are excluded.

(a) Is there a diurnal pattern in 3M stock trading? You may construct a time series \(n_{t}\), which denotes the number of trades in a 5-minute time interval to answer this question.

(b) Use the price series to confirm the existence of a bid-ask bounce in intraday trading of \(3 \mathrm{M}\) stock.

(c) Tabulate the frequencies of price change in multiples of tick size \(\$ \frac{1}{16}\). You may combine changes with 5 ticks or more into a category and those with -5 ticks or beyond into another category.