In one sentence — Hurst separated 884 weekly Dow closes from 1935–1951 into six components and stated that their sum reconstructed the index within ±1%. This is a result on the same sample used for the analysis, not an out-of-sample forecast error.
What does Hurst's DJIA decomposition show?
Fig. IX-4 of The Profit Magic of Stock Transaction Timing places the DJIA, six curves extracted with numerical filters, and several World War II events on one sheet. Hurst presents it as the product of more than three million computations and as an internal demonstration of his cyclic interpretation.
The figure matters because it makes a difficult idea visible: a complex movement can be described as a sum of oscillations at different scales. Describing an observed series closely and forecasting a future series are, however, different tasks.
The six scales, without formulas
The four shorter components have reported average durations of 9.6, 19.85, 34.6, and 67.98 weeks. The arithmetic in the book is consistent with the oscillation counts over 884 weeks: 92, 44.5, 25.5, and 13 samples respectively.
The fifth component represents the nominal family near 4.5 years. Hurst does not find a fixed duration: he lists samples of 38, 43, 28, 54, and 58 months. In the 1942–1944 stretch, the shortest duration coincides with near-zero amplitude; the author treats this as an example of his variation principle.
The first curve collects oscillations longer than 54 months and the underlying movement. Hurst marks two highs, A and C, and two lows, B and D, linking them to the nominal family near nine years. These labels describe the author's historical model; they are not immutable periods or proven universal laws.
What ±1% actually means
Hurst states that the sum of the six components reproduces the DJIA closes within ±1%. The statement measures the quality of the in-sample reconstruction from which the components were identified and extracted.
It does not measure the distance between a real-time forecast and a later price. It does not report how many filters or periods were tried, compare the method with a simple benchmark, or apply a frozen rule to untouched data. The ±1% is therefore not a forecast error and not independent validation of market predictability.
That distinction does not make the figure useless. It makes it legible for what it is: a close retrospective decomposition and an internal coherence check of Hurst's model.
The fall of France and the eight cases
Hurst examines three vertical lines before the fall of France in May 1940. In his reading, at the third date five components point down while one is flat, so the sharp decline is consistent with the state of the already extracted curves.
The author repeats the same scorecard for eight turns between 1935 and 1951 and interprets each case through component direction, phase, and amplitude. This is a consistent narrative check on the chart, but the cases are selected and explained after the whole period has been observed. The plate does not document a forecast recorded before the events or a complete inclusion rule for every comparable turn.
The war dates are retrospective annotations too. A filtered curve appearing to fall before an event does not establish that the news had no effect, nor does it identify the cause of the move by itself.
What the figure does not prove
Fig. IX-4 does not show that the six components are the only possible decomposition, that the residual is random or non-random, that the durations persist in every era, or that the same result holds for every security. Above all, it does not separate model construction from testing: one history is reused both to choose the representation and to assess its fit.
This is the issue now called data snooping: impressive results can arise when previously examined data also guide model selection. It does not mean the result is false; it means predictive ability must still be measured elsewhere.
What a modern test would look like
Periods, filters, phase rules, and turning-point criteria would first be fixed using only an initial training segment. The model would then be applied without correction to a later out-of-sample period. Reconstruction and forecasting would have separate metrics; forecasts would be compared with simple benchmarks and would report adverse windows, instability, and trading costs as well as successes.
Until that step is performed, the precise reading is: Hurst reports a reconstruction within ±1% for the 1935–1951 DJIA; Fig. IX-4 does not measure out-of-sample forecasting skill.
Sources
- J. M. Hurst, The Profit Magic of Stock Transaction Timing, Prentice-Hall, 1970, Chapter 9, pp. 151–157, Fig. IX-4 — sample, components, durations, ±1%, fall of France, and eight cases.
- Google Books bibliographic record for the 1970 Prentice-Hall edition.
- Halbert White, “A Reality Check for Data Snooping”, Econometrica, 68(5), 2000, pp. 1097–1126 — why selection and evaluation on the same data do not establish predictive superiority.
Connections
- Nominal cycles — duration families and variation
- Spectral analysis — how periodicities are sought
- Ormsby numerical filters — how Hurst isolates bands
- Historical events and cyclicity — events, counterfactuals, and causation
- Hurst tradition — complete historical path