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James Marsden Hurst 1924—2005 Biography and works
Chapter 3.7 — Verify Your Chart Patterns

Moving averages as filters in Hurst's method

Hurst uses moving-average span to attenuate short components and centers the result in time; this entry separates the historical filter from information lag and its limits.

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

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In one sentence — A moving average replaces each price with an average over a window: it smooths some oscillations, but once centered in time its latest values cannot yet exist.

What does a moving average do?

A simple moving average of span N takes N consecutive observations and computes their mean. The result changes less rapidly than the original series because positive and negative deviations partly offset one another. Span is therefore a filter choice: a wider window tends to produce a smoother curve but loses more local detail.

In Hurst’s language, the purpose is to attenuate short components so longer ones can be seen more clearly. His Appendix IV links span to the average’s response to sinusoids.

Smooth, center, accept the trailing gap 31 hypothetical observations and an 11-value centered arithmetic average; the final 5 positions have no average calculable from the available data. A centered average is descriptive 31 hypothetical observations · N=11 · 5 final positions without an average FINAL 5 no average Centered for analysis · unavailable at the right edge Cyclepedia diagram · Emiciclo
Hypothetical example: 31 observations and an 11-value centered average. Five final positions have no calculable average; the line is computed from the plotted prices.
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Span and response: the precise version

For a sinusoid sampled at regular intervals, a simple average of N ≥ 2 values has a zero at period N, expressed in sampling intervals: a window covering one complete turn averages its positive and negative parts. Its full response is not a sharp switch, however. It depends on frequency and includes other zeros and side lobes; it is inaccurate to say that every shorter fluctuation is always removed or every longer fluctuation passes unchanged.

This qualification does not erase the historical use. It clarifies that “cutoff” is a practical simplification. To know how much a periodicity is attenuated, one must examine the filter response rather than compare its duration with N alone.

Why Hurst discusses 10 and 30 weeks

Within the book’s nominal framework, the 10-week average lies between components of about 6.5 and 13 weeks, while the 30-week average lies between roughly 26 and 39 weeks. Hurst reads the empirical popularity of these spans as consistent with his proposed separation of scales.

They are historical examples tied to his model, not universal parameters. Data frequency, market, objective, and component stability all change observed behavior. Span should be declared before analysis and compared with alternatives.

What does “centering” mean?

A centered average places the arithmetic mean at the midpoint of the observations used. For regularly spaced data, with N = 2k + 1 equally weighted values:

CMAₜ = (Pₜ₋ₖ + … + Pₜ + … + Pₜ₊ₖ) / (2k + 1)

It requires k observations before and k after the center. With N = 11, that is five on each side. If the latest available observation is T, the latest calculable centered average is at T − 5; the average at T still requires observations from T + 1 to T + 5. Centering the drawing does not make those data available earlier. Extrapolating the final segment remains a forecast, separate from the observed average.

With even N, the midpoint falls between two observations: for the ten values from Pₜ₋₉ to Pₜ, it is t − 4.5. To align the result with observed timestamps, NIST shows a second average of two consecutive averages: this is an additional convention that changes the effective weights and must be stated.

Hurst recommends odd windows and, in Appendix IV, p. 208, gives the lag as L = [(n − 1) / 2] × t_n, where t_n is the time spacing between observations. The description of Alloys Unlimited on p. 65 instead specifies a shift of five and a half weeks for the ten-week average. These formulations do not coincide: the discrete count made explicit here follows observation indices, without treating that narrative value as a general rule.

Proper use and operational limit

A centered average is useful for historical analysis, scale study, and envelope construction. An uncentered average can be calculated in real time but retains phase lag. Comparisons are meaningful only when timestamp, span, calculation rule, and data availability are stated.

Evidence boundary — Smoothing is not forecasting. Centering improves descriptive alignment but leaves a trailing gap; any value inserted there is an estimate, not an already observable moving average.

Sources

  • J. M. Hurst, The Profit Magic of Stock Transaction Timing, Prentice-Hall, 1970, Ch. 3, pp. 62–66, Figs. III-10 and III-11; Appendix IV — span, 10- and 30-week examples, and time centering.
  • NIST/SEMATECH, Moving Averages, e-Handbook of Statistical Methods — definition and smoothing role of moving averages.
  • NIST/SEMATECH, Centered Moving Average, e-Handbook of Statistical Methods — centering and even-length windows.
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