Consider again the transactions data of 3M stock in December 1999.

(a) Use the data to construct an intraday 5-minute \(\log\) return series. Use the simple average of all transaction prices within a 5-minute interval as the stock price for the interval. Is the series serially correlated? You may use Ljung-Box statistics to test the hypothesis with the first 10 lags of the sample autocorrelation function.

(b) There are seventy-seven 5-minute returns in a normal trading day. Some researchers suggest that the sum of squares of the intraday 5-minute returns can be used as a measure of daily volatility. Apply this approach and calculate the daily volatility of the log return of \(3 \mathrm{M}\) stock in December 1999. Discuss the validity of such a procedure to estimate daily volatility.