The file mmm9912-dtp.txt contains the transactions data of the stock of 3M 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 pm Eastern time are excluded.

(a) Is there a diurnal pattern in 3M stock trading? You may construct a time series nt, 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 3M stock.

(c) Tabulate the frequencies of price change in multiples of tick size

$1/16. You may combine changes with 5 ticks or more into a category and those with −5 ticks or beyond into another category.