Cycle Analysis Basics

The application of cycles to market forecasting rests on Fourier Theory which implies that all market behavior (or any continuous mathematical function) can be explained as the sum of a number of cycles with a known frequency.

The analysis of market cycles has a long history but much of the current theory and practice was pioneered by an aerospace engineer, Jim Hurst, in the late 1960’s and early 1970’s, analyzing long series of price data on an IBM mainframe.

Key Cycle Definitions

Cycle:

  Where a series starts low, increases smoothly to a high and descends smoothly in approximately the same length of time as the increase to another low

Periodic Cycle:

  Where the cycle is repeated in the same approximate time (known as the duration, frequency or cycle for shorthand)

Phase:

  The direction in which the cycle is heading: either an up-phase or a down-phase

Amplitude:

  The estimated price movement attributable to a cycle that can be used to estimate targets for profit taking on positions. The general rule is the greater the cycle duration, the greater the amplitude

Proportionality:

  Cycle amplitude is proportional to duration

Some Principles of Cycle Analysis

Summation:

  A restatement of Fourier Theory by Hurst. Cycles are additive which means that if all individual periodic cyclical components can be isolated they can be summed together in terms of phase and amplitude and the price motion forecast. For a graphic illustration how cycles nest and interact please click here.

Understanding the interaction between two or more dominant cycles of varying duration is the key to being able time entry and exit points and, as far as possible, we always try to identify at least two dominant cycles in each sector.

Normality:

  Individual issues and sectors tend to follow certain nominal cycle periods which is an expression of the principal of Commonality. Hurst described a number of common nominal cycle periods many of which we have been able to confirm through the observation of sector cyclicality in our database. For the purpose of our Traders' Edition Newsletter, we generally limit discussion to the following cycle periods and shorthand grouping:

• Long cycles:

    6 months+

• Intermediate cycles:

    12-14 week, 6-8 week

• Short term:

    Less than 5 weeks

In our Market Navigator web-based research product, what we identify as “long” or “short” cycles can fall into the category of “intermediate cycles” above.

Translation:

  Whereas a sine wave is completely regular in its movement market cycles rarely behave in this way. Instead the cycle peak or maximum is usually shifted in time from the theoretical midpoint of the cycle. As a rule of thumb left translation (where the peak arrives prior to the cycle mid-point) is viewed as bearish, and right translation is viewed as bullish.

Cycle Inversion:

  Occasionally, cycles may invert where a projected low instead becomes a high. This is a feature usually seen when longer cycles reverse. For example, a 4-week cycle may invert as a longer 6-month cycle turns down.