Problem

Using the bars from exercise 4:

(a) Sample bars using the CUSUM filter, where {yt} are absolute returns and h = 0.05.

(b) Compute the rolling standard deviation of the sampled bars.

(c) Compare this result with the results from exercise 4. What procedure delivered the least heteroscedastic sample? Why?

Exercise 4

Form E-mini S&P 500 futures dollar bars:

(a) Compute Bollinger bands of width 5% around a rolling moving average. Count how many times prices cross the bands out (from within the bands to outside the bands).

(b) Now sample those bars using a CUSUM filter, where {yt} are returns and h = 0.05. How many samples do you get?

(c) Compute the rolling standard deviation of the two-sampled series. Which one is least heteroscedastic? What is the reason for these results?