The indices, led by the S&P 500 and the Nasdaq 100, continue their relentless push higher. The chart below of the ES futures includes the 10 week and 20 week price waves based on bandpass filter analysis from the prior 4 year low in November 2012 to today. The 20 week wave continues to create higher lows and higher highs. All of the price waves from the 80 week down to the 10 week are showing the textbook geometric relationship straight out of Hurst’s cycles course. Unfortunately that is not always the case, at least from a filter analysis standpoint. After the February 2014 80 week low phasing was a little more difficult due to increased modulation of the 10 week wave amplitude from May through July. The decrease in amplitude caused the duration of the waves to shorten.
Some analysts may have had a little difficulty phasing the 20 week wave after the February low due to the duration fluctuation of the waves. David Hickson in his most recent post gives an excellent review of some of the alternatives using the Sentient Trader software. Bandpass filter analysis offers another subtle solution. The difficulty is caused by the prominent low the second week in April. As David pointed out, the time from the February low to the April low is too short to be a 20 week wave and the time from the February low to the August low is too long to be a 20 week wave. So what is the appropriate solution?
The chart below may offer some insight. It is a daily chart of the ES futures with the 40 day price wave extracted with a filter based on the same nominal model in use for years. It subdivides the time from the February low to the August low in to eight sections, the geometric series of Hurst’s simplified harmonic model. Notice that the mid-April low is the third oscillation from the February low followed by a slight duration fluctuation caused by a diminution of the wave amplitude. If one follows a strict application of Hurst’s simplified harmonic phasing model, the 80 day lows would be “pinned” at every other low of the 40 day wave beginning at the February low, and the 20 week low would be “pinned” at the May low of the 80 day wave. This also identifies the February and August lows as 40 week lows.
The moral of the story is that visually prominent absolute lows are not always the best lows for phasing purposes of longer waves due to duration fluctuations caused by amplitude modulation. Instead of using a top-down approach to phasing, it is sometimes advantageous to phase the shorter waves first in these situations. There will be occasions when this approach results in a complex harmonic relationship among the waves, but the phasing will be very accurate.