Problem

On a series of E-mini S&P 500 futures tick data:

(a) Form tick, volume, and dollar bars. Use the ETF trick to deal with the roll.

(b) Count the number of bars produced by tick, volume, and dollar bars on a weekly basis. Plot a time series of that bar count. What bar type produces the most stable weekly count? Why?

(c) Compute the serial correlation of returns for the three bar types. What bar method has the lowest serial correlation?

(d) Partition the bar series into monthly subsets. Compute the variance of returns for every subset of every bar type. Compute the variance of those variances. What method exhibits the smallest variance of variances?

(e) Apply the Jarque-Bera normality test on returns from the three bar types. What method achieves the lowest test statistic?