Harmony

Revealed
By Steven J. Grisafi, PhD.

As explained in the previous analysis Periodicity there is an inherent regularity present in the harmonic analysis of financial price data resulting from the reporting schedule of the data. This regularity needs to be subtracted from the Fourier spectrum for any financial instrument in order to reveal the true market periodicity of the instrument caused by investor choices. Grisafi Rheomonics is pleased to announce the Regularity analysis which has been designed to help investors remove this regularity from financial harmonic analysis to reveal true periodicity.

Within the new analysis offering there are posted four graphs each accompanied by the Fourier coefficients used to plot the graphs. Although a business week is usually only 5 days per week, because financial markets operate throughout the world on this schedule, Grisafi Rheomonics evaluates data six days per week for such markets. The advent of cryptocurrency, caused by the development of Bitcoin, has created a financial market that operates continuously seven days per week. Therefore, both the Time Schedule Chronology and the Price Data Chronology harmonic analysis need to address the possibility of a seven day per week reporting period as well as the more customary six day per week reporting period.

A cursory examination of the graphs on the Regularity page reveals a few pertinent facts. First, the Time Schedule Chronology graphics will remain constant. The graph for the seven day per week reporting period regularity will always have a constant amplitude negative 183. Actually, the amplitude for the seven day reporting period of the Time Schedule Chronology will always be negative one half of the number of days in the year. The year 2020 was a Leap year so it currently shows exactly -183. The six day per week reporting period for the Time Schedule Chronology reveals the origin of the peaks seen in the Periodicity article. The peak at a period of approximately 55, and then repeated at approximately 110 days, is, as was suspected before, an artifact of the time schedule reporting period.

Although the Time Schedule Chronology graphs will remain constant, the Price Data Chronology graphs will change with the addition of each new data point. This may seem unusual but it occurs because of the permutation of the days compromising the time schedule. Consequently, while the daily change may be imperceptible, it is real. Thus, the Regularity analysis will be updated daily.

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