Problem

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

(a) Quantize the returns series using the binary method.

(b) Quantize the returns series using the quantile encoding, using 10 letters.

(c) Quantize the returns series using the sigma encoding, where σ is the standard deviation of all bar returns.

(d) Compute the entropy of the three encoded series, using the plug-in method.

(e) Compute the entropy of the three encoded series, using kontoyiannis' method, with a window size of 100.