Caption: Figure 16: Emergence of soliton trains according to KdV2 from initial cosine wave
. A = 0.3, T = 50.
Figure 19 indicates that the cosine waves
for -21 degrees and that for 0 degree are nearly the same phases because the amplitude of the addition of the two waves is above 1 N, whereas the cosine waves
for -34 degrees and that for 0 degree are nearly reverse phase because the amplitude of the addition of the two waves is below 1 N.
Specifically, under the assumption that each high-frequency stock return is an event that triggers momentum and reversal periodically, we decompose each future return into a collection of decaying cosine waves
that are functions of past returns.
For example, the increasing-frequency (up-chirp) waveform, shown in Figure 11, was produced by applying a narrow pulse to the input of an ACT filter in which the taps had been loaded with a Hanning-weighted cosine wave
with a frequency sweeping from 5 MHz to 60 MHz.
(8.) Formally, I regress the data on a series of cosine waves
as described in Muller and Watson (2008, 2015).