The first of these indicators I call an INSTANTANEOUS TRENDLINE. It works because it completely removes the dominant cycle from a smoothing average.
For the mathematically inclined, the Fourier Transform of a rectangular window (formed by a simiple average) is a Sin(X)/X distribution. The objective is to place the first null of this distribution exactly at the dominant cycle. For the intuitively inclined, what we are doing is taking
a simple average over the full dominant cycle period. In such an average, there are as many sample points above the midpoint as below the midpoint with the result that the sum of all these sample points is zero. The next indicator is created by taking a moving average over half the period of a dominant cycle. In this case, the amplitude of the dominant cycle is attenuated by exactly 2/PI. Our objective is to restore the full amplitude of the cyclic portion. So we take this latest moving average, subtract the “Instantaneous Trendline”, multiple the difference by PI/2 (1.57 approximately), and then add the Instantaneous trendline back. Since the lag of a moving average is about half the moving average window length, this modified half dominant cycle moving average will still lag the realy cyclic swing by a quarter cycle.