2004issue C051-6
Build a phase-change index as a reversal rule
A phase-change index is built from closing-price deviations around a lookback gradient line and stays bounded between 0 and 100. Period momentum supplies the slope sign the index does not carry, so long, short, and hold rules can be written and tested as one next-open reversal procedure.
- The phase-change index is 100 times the sum of up deviations from the lookback gradient line, divided by the sum of up and down deviations, so it is bounded between 0 and 100.
- Period momentum is the current close minus the close at the start of the same lookback and supplies the gradient-line slope sign that the index does not encode by itself.
- Long setups need positive momentum and a reading below 20, short setups need negative momentum and a reading above 80, and the two consolidation transitions are treated as hold.
- The default 35-day rule is a next-open reversal that keeps the existing position unless the opposite condition appears, and any later amendment is to be retested as a whole system.
Construct the oscillator from a gradient line
The phase-change index is an oscillator bounded between 0 and 100. It is constructed as 100 times the sum of up deviations from the lookback gradient line, divided by the sum of up and down deviations.
The gradient line is the imaginary straight line connecting the first and last closes of the chosen lookback. An up deviation is the amount by which a close sits above that line on that day. A down deviation is the amount by which a close sits below it.
Add period momentum for slope
The index does not encode the sign of the gradient-line slope by itself. Period momentum is the current close minus the close at the start of the same lookback, and it supplies that sign.
Together the two readings describe both the slope of the line and whether most closes sit above or below it.
Turn six transitions into long, short, and hold
Six phase transitions are distinguished by combining gradient-line slope with whether most closes sit above or below that line. Long setups are the two cases with positive momentum and a phase-change index below 20. Short setups are the two cases with negative momentum and a phase-change index above 80. The two consolidation transitions are treated as hold.
Readings above 80 or below 20 are interpreted as a phase change inside the window. Readings between 20 and 80 are interpreted as the current phase remaining in force. Those bands are the default phase-change thresholds.
State the default next-open reversal
The default trading rule is a next-open reversal that uses the 35-day default lookback for both readings. Go long when today's 35-day momentum is positive and 35-day phase-change index is below 20. Go short when today's 35-day momentum is negative and 35-day phase-change index is above 80. Otherwise keep the existing position.
That procedure is a reversal system: it is always long or short and never flat, flipping only when the opposite entry condition appears. The published construction has no money-management stop-losses or trailing stops.
Read the worked five-day case
The worked five-day example produces a phase-change index of 7.23 and a positive momentum of 1.8. That pair maps onto the long-side phase-change cases rather than a hold.
Check length and markets as one system
The historical test framed the phase-change index as a never-flat reversal system on 35 markets from 2 January 1980 through 30 April 2003. It used one contract per signal, deducted 75 per trade, and closed open trades at the final day's close.
A five-length parameter check used 22, 28, 35, 42, and 50 days, with all other test settings unchanged. That robustness grid was used to argue that the default 35-day length was not an isolated fit. Every tested length was profitable on the same portfolio.
Across those five lengths, 26 of 35 markets were profitable at the default setting. The weakest year-count result was 17 profitable years out of 23, and the strongest was 20 of 23.