Skip to content
CyclepediaThe trading encyclopedia
SESSION
ITENESPT-BRFRDE

Appendix I — The DJIA spectrum according to Hurst

Data, filters, and limits of Hurst's spectral analysis of 2,229 weekly Dow Jones Industrial Average observations.

Cite this entry

This reference cites the Cyclepedia entry. The documents it draws on are listed in the entry’s sources.

On this page

In plain language — Hurst searched the Dow for oscillations recurring at recognizable intervals. The result is his historical estimate, not proof that markets contain fixed or immediately tradable frequencies.

Appendix I · the proposed spectral signature Explanatory diagram of Hurst’s reported results, not a reconstruction of the original data. The document proves that Hurst made the claim; the claim still requires independent testing. HURST 1970 · APPENDIX I Appendix I · the proposed spectral signature Explanatory diagram of Hurst’s reported results, not a reconstruction of the original data CYCLEPEDIA DIAGRAM — EMICICLO 0 2 4 6 8 10 frequency — radians/year 0.3676 SAMPLE 2,229 closes weekly DJIA · 1921–1965 INTERNAL CHECK Fourier + filters methods in the same study BOUNDARY not external replication author claim to retest The document proves that Hurst made the claim; the claim still requires independent testing.
A teaching reconstruction of the procedure, not a digitization of the original plate. Tap or select an area to separate data, method, result, and limit.
Select the highlighted points to explore the detail

Data and question

Appendix I uses 2,229 weekly DJIA closes from 29 April 1921 through 25 June 1965. It asks whether such a long series concentrates energy around certain frequencies rather than spreading every movement indistinctly.

A high frequency represents shorter oscillations and a low frequency longer movement. A spectrum can organize that distinction; by itself, it does not date the next trough.

Hurst’s procedure

Hurst describes coarse- and fine-resolution analysis using numerical filters and comb filters. He compares filter output while changing tooth spacing, seeking configurations compatible with a family of spectral lines.

The book reports a characteristic spacing of about 0.3676 radians per year and interprets some lines as a harmonic structure. These are the author’s results from his own procedure. Cyclepedia does not present them as independent replication or as universal parameters that can be transferred without new testing.

How to read it today

The appendix’s historical value is its attempt to make a cyclic hypothesis testable with data, filters, and an explicit procedure. Its limitations matter just as much: filtering, detrending, sample edges, resolution, and parameter choice can all change a spectrum. Searching more frequencies also increases the risk of finding an unstable pattern in hindsight.

A modern check would pre-register transformations and criteria, compare the output with surrogate and noise series, quantify frequency uncertainty, and test stability out of sample. Only then would an operational interpretation become meaningful.

What it establishes — and what it does not

The appendix establishes that Hurst applied this procedure to that sample and published those results. It does not establish that every security shares the spectrum, that the lines remained stable after 1965, or that they produce an advantage after costs. Appendix II makes a separate attempt at generalization and needs its own limits.

Sources

Suggest an edit My proposals