Scale-free Commodity Channel Index construction

Construction as a scaling problem

Editorial reading: oscillator construction here is a scaling problem. Once a cycle length is assumed, typical price, a simple moving-average benchmark, and an adaptive variability divisor convert raw ticks into a channel that can be compared across contracts.

The Commodity Channel Index is built as a timing tool for markets already treated as seasonal or cyclical. It does not estimate cycle length.

Typical price as the session input

Each session is reduced to a typical price equal to one-third of the high, low, and close. Typical price is the ordered price input to the channel index.

A simple moving-average benchmark

Current price is compared with a simple moving average rather than an exponentially smoothed average so the benchmark updates and distant history does not dominate present patterns. A moving average of those typical prices is then formed over N sessions.

Why the divisor has to adapt

A daily-limit divisor is rejected because an equal-sized price move does not always have the same significance. The divisor must stay small in quiet oscillation and grow when a breakout appears.

Mean deviation is the selected divisor after alternative divisors were tested. It is the average absolute gap between recent typical prices and their moving average, used as a variability divisor that widens when prices break out. A mean absolute deviation of those typical prices is formed over the same N sessions. The daily calculation is described as impractical to perform by hand.

Scaling the gap into a channel

The index equals the gap between today's typical price and that moving average, divided by 0.015 times the mean deviation, so that 70 percent to 80 percent of random fluctuations fall inside a plus-or-minus 100 channel.

Published setup rules

In the published construction, a reading above +100 marks a long setup and a return below +100 closes that long, with a symmetric pair of rules at -100. The thresholds can be changed.

Data-base length is the critical choice

Lookback length is the critical construction choice. Data-base length is the number of sessions in the moving average and mean-deviation windows. A short data base treats ordinary daily fluctuation as cycle turns, while a long data base delays breakout recognition.

On a theoretical perfectly cyclic contract, a 10-day data base detected cycle tops well but breakout detection weakened on short cycles. Tests with 5-, 15-, and 20-day bases suggested the data base should stay shorter than one third of the assumed cycle length.

A 20-session data base was adopted as the standard program length, with allowable windows from 5 to 25 sessions, after a 5-session window was judged more exposed to whipsaws despite stronger theoretical detection on the cyclic test series.