**The Hurst cycle designates a method of technical analysis based on the use of cycles. Hurst cycles are not widespread in Europe to date and are mainly used by rare analysts in the United States. Hurst’s cycle theory was however developed in the 1970s by engineer JM Hurst. JM Hurst is the author of several books, the most famous of which is The Profit Magic of Stock Transaction Timing which was published in 1970. Unfortunately, like William Gann before him, his methods remain complex and little known to the general public. In recent years, authors such as Christopher Grafton have attempted to democratize the analysis of Hurst cycles (Mastering Hurst Cycle Analysis, 2011). Today, some analysts use Hurst cycles on assets like gold or Bitcoin, which we will focus on here. **

## fundamental principles

What is a cycle? In financial markets, fluctuations in asset prices can be considered as cyclical phenomena. Indeed, a cycle is defined in mathematics according to three parameters:** amplitude, period and temporality**.

The amplitude is the height that separates the low point of the cycle from the highest point. The periodicity designates the period over which a complete wave is traveled (difference in time between two low points). Finally, temporality designates the moment when the peak is observed. The five fundamental principles set out by Christopher Grafton in *Mastering Hurst Cycle Analysis *for cycle analysis are:

- First of all,
**harmony**. The harmonic principle, also used in music, refers to the fact that all cycles are linked together. Let’s say for simplicity that a 10-year cycle can be broken down into two 5-year cycles, or three 3.3-year cycles. - Secondly,
**synchronicity**. The synchronous principle means that the turning points of the cycles generally take effect at the same time. Most often, it is the low points of the cycles that take effect at the same time. The synchronicity of the cycles explains the precision of the points of the market turning points. - Thirdly,
**infinity**. JM Hurst spoke of a “nominal model” to describe the fact that cycles can be broken down on an infinite time scale. There are an infinite number of cycles on infinitely short or infinitely long time scales. - Fourth,
**variability**. The cycles are themselves variable over time. The cycles can vary themselves according to cyclic logics. It can be a change in the periodicity of the cycles, their amplitude or their temporality. - Finally,
**universality**. These last four principles are applicable to all markets.

## Valid Trend Lines (VTL)

This principle combines channel and cycle analysis in technical analysis. Valid trend lines, Valide Trend Line in English (VTL), more simply designate the way in which cycles of different periods interact. The Hurst trendline is a resistance or support that is validated if an asset cycle has validated at least two highs or two lows on this trendline.

The chart above shows the price of Bitcoin (black) and the four major Bitcoin cycles we had identified. How then can we construct a valid trend line? A resistance is valid if it is hit by two highs in a given cycle. When the resistance is broken, the next cycle (with a larger period) is considered to change its trend. Shown in green is a resistance validated by the 1.2-year cycle in 2018 and 2019. This resistance was broken at the end of 2020, which indicated a bullish breakout of the following cycle (1.6 years). We could therefore expect a strong upward acceleration in the price. The next resistance target was therefore at least until the next 1.6-year cycle high in early 2021.

Similarly, we have depicted in red support validated by two 1.6-year cycle lows in early 2020 and late 2021. This support line was broken in early 2022. bottom of the next cycle (2.4 years). The next low of the 2.4 year cycle is expected to take effect in the summer of 2022. The construction of valid trendlines allows the construction of relevant resistances and supports according to cyclical criteria.

## Hurst cycles and moving averages

We have seen that when a short cycle breaks a resistance or a support, it means that the long cycle has validated a low point or a high point. We can then respectively expect a top or a bottom according to the long cycle. However, the mathematical identification of cycles remains complex and the use of graphical analysis can simplify the vision of cycles. Generally, the price of an asset can be broken down into a minority of highly influential long cycles and a majority of weakly influential short cycles. Thus, it may be useful to disregard short cycles. Hurst’s method was to use the moving average (centered) to retain only long cycles.

The graph above illustrates our analysis. Bitcoin’s 50-day moving average is shown in red on the chart. In addition, the gray scale at the bottom of the graph illustrates the absolute difference between the price of Bitcoin and its 50-day average: this is the influence of short cycles. Ultimately, the difference between the stock market price and the long average always tends towards 0, because long cycles always have more influence than short cycles. Finally, we added the blue curve which is the combination of the four cycles that we have represented in the analysis of valid trend lines.

Moreover, the comparison of the same blue curve with the moving average at 6 months shows an even stronger correlation. However, modeling by only 4 cycles in blue does not give us exact accuracy relative to the moving average. But we can nevertheless notice the presence of four major cycles since 2017 with 4 minimums of the moving average. Additionally, Hurst used a channel around the mean to represent extremes like Bollinger bands.

## Measure Hurst cycles graphically

Furthermore, Hurst cycles are based on the harmonic principle. Indeed, Hurst considered a main cycle lasting 54 years, close to the Kondratiev cycle in economics. This 54-year cycle can be broken down into three 18-year cycles or six 9-year cycles (Juglar cycle). Consequently, we can apply the same process to obtain the cycles over periods of a few weeks and so onâ€¦

Cycle No. | Years (period) | Month (period) | Weeks (period) |

1 | 54 | ||

2 | 18 | ||

3 | 9 | ||

4 | 54 | ||

5 | 18 | 80 | |

6 | 9 | 40 | |

7 | 20 | ||

8 | 10 |

*Mastering Hurst Cycle Analysis*Christopher Grafton.

The classic method used to analyze cycles in a simple way is to measure the distance between two low points for each phase. Once a number of phases have been measured, the average of the observed periods is averaged. A more or less relevant cycle is then obtained from the graphical analysis. However, this technique is simpler and less precise than mathematical analysis.

Let’s take the example of the phases observed on Bitcoin since 2017. We observe three fully validated phases where we note two minimums: a phase of 1.57 years, 1.2 years, and 1.27 years. The average of these phases is therefore 1.35 years (40 phases of 1.35 years make 54 years). This period is close to our study with the observation of two cycles of 1.23 years and 1.64 years (average period of 1.43 years). We can therefore hope that the next low point of this medium-term cycle will take effect around the last two months of 2022. This is also in line with the analysis carried out during our previous publications and conferences.

## In conclusion

In short, we have seen in this first article dedicated to Hurst how cycles can be fundamentally applied to technical analysis. First, the use of valid trend lines allows a much more relevant analysis of market reversals. Adding cyclical criteria to supports and resistances makes price analysis more concrete over time. Next, the use of moving averages allows us to identify the major underlying cycles during an asset. It is then easier to notice the long cycles that affect prices. In the case of Bitcoin, this shows us that the asset is determined in the medium term by a cycle of 1.35 **year which includes the combination of other cycles. **

Finally, the last few months have effectively demonstrated the existence of a bearish cycle that we have been identifying since last year. Nevertheless, the relatively weak history of long cycles does not allow us to project the long-term future of market forces. But Hurst cycles are a method of analysis that can prove to be considerably powerful with a little technique. Several analysts in the US or on the networks offer extensive Hurst analysis on Bitcoin and most other assets. It is important to note that we have here **coupled Hurst’s analysis with traditional mathematical analysis. **

**This method of generalizing cyclic mathematics to technical analysis, developed in the 1960s and 1970s, has not finished revealing all its secrets… We will endeavor to explain the other principles of the analysis of the engineer JM Hurst in future publications. Reference books on the subject are Mastering Hurst Cycle Analysis (2011) and The Profit Magic of Stock Transaction Timing (1970).**

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Thomas Andrieu

Author of several books, economic and financial editor on several sites, for many years I have developed a real passion for the analysis and study of markets and the economy.