Trend Lengths and the Ichimoku Time Element

When Goichi Hosoda (Ichimoku Sanjin) developed the methodology known as Ichimoku Kinko Hyo, he started with a chart framework and developed three main areas: Wave Structure, Prices Projections and the Time Element. This paper presents a study on trend lengths in the equity market and relates it to the time periods observed by Hosoda.

The time element in the Ichimoku Kinko Hyo methodology

The three main elements in the Ichimoku Kinko Hyo Japanese analytical method are Time, Waves and Price Levels or Projections. These are imbued in a framework consisting of a candlestick chart with three additional elements plotted through five lines.

According to Hidenobu Sasaki, the essence of the method is the Time Theory and, in a way, on a daily chart, the movement develops according to a specific “wavelength”. This wavelength — Hidenobu thought there were relationships between physical cycles and this wavelength — generates some specific periods for which Hosoda established the duration.

According to Hosoda, the market does not fluctuate as time goes by, but it is Time the element that determines the structure of the fluctuations.

Basic Numbers

When looking at price movements in the Japanese market, Hosoda established the concept of Basic Numbers, both Simple and Compounded, the latter generated by combination of other cycles. Hosoda divided movements according to their duration and labelled them against this table.

The compounded numbers are built by combining the simple ones, subtracting the linking day or days:

• 33 = 17 + 17 − 1
• 42 = 17 + 26 − 1
• 65 = 33 + 33 − 1
• 76 = 26 + 26 + 26 − 2 — three stages, a complete turn

According to the Basic Numbers projection method, the time periods corresponding to the basic numbers would represent points where the probability of a trend reversing increases — although the opposite effect would occur in some cases, gaining momentum.

Taitou-Suchi: equality in the numerical values

Beyond projecting the basic numbers forward, the time theory also looks for equality between intervals that have already occurred. Two methods are used:

• Hen-Gi — taking a numerical value that happened before and applying it from another point.
• Jyu-Gi — taking a numerical value that happened before and applying it from a point inside the first interval.

The time theory may be used in combination with the price and wavelike theories because by itself it would be limited.

How the trends were measured

One of the critical points when conducting studies on technical patterns is how to measure trends. Bulkowski (2007), for example, uses a 10-day exponential moving average as a starting point and seasons it with special rules to allow price trends of one or two days to override the result.

For this research I decided not to use technical indicators, but to try a different method, with excellent results: an automatic denoising process of a one-dimensional signal using wavelets. All wavelet transforms may be considered time-frequency representations. Coefficients from 1 to 6 were employed in order to obtain shorter to longer term trends.

The study

There is a double goal in this research. First, carrying out a measurement of the lengths of trends in the market movements to ascertain the validity of a division in time cycles as determined by Goichi Hosoda. Second, a comparison among those lengths proposed by Hosoda and the ones empirically observed in the sample.

The sample covers the trend lengths of the S&P 500 and EuroStoxx 600 components, from 1998 to mid-2014. Splitting the daily chart trends into six levels, from shorter to longer term, gives a fast first level with an average length of four days and an average return of 5%. Level 2 is similar, with an average return of 6% and an average length of five days. The returns in level 3 and level 4 trends are 8% and 12% respectively.

The choice of sample will always introduce a bias into the results, so these figures are better taken as one more approximation than as absolute values.

Trend lengths by level

Statistical mode of simple trend lengths on daily charts, in days, across the six levels:

The original paper also tabulates Double AB trends (two consecutive trends), Double AC trends (two alternate trends) and Triple ABC trends (three consecutive trends), each showing the most repeated length value.

Findings

Among the key findings about trend lengths is the fact that starting at level 3, there are differences between uptrends and downtrends. The bearish trend mode is eight days in level 3 and 13 days in level 4, while bullish trends show a mode of nine days in level 3 and 18 days in level 4.

Analyzing the data, it appears that the “wavelength” identified by Goichi Hosoda fits better with a level 3 or level 4 coefficient than with lower or higher levels. The mode length in a level 3 bullish trend is nine days — the length that Hosoda called a period. The level 3 bullish trend length histogram closely resembles a gamma distribution.

Joining level 3 uptrends, the mode is found at 24 days, two days below the basic number 26. For bearish trends it is only 13 days, a value often seen in the double combinations at level 2 and which, without assuming an explicit value in the Ichimoku time model, is mentioned by Hidenobu Sasaki as half a stage.

Connecting several level 3 trends, in the case of a triple combination 33 days may be extended up to 38 when combining two uptrends with an intermediate correction, which may be due to the extension effect commented by Higashino (2014). There are also interesting values in level 4 uptrends: 42 days, equal to the basic compound number of one stage and two periods, and 78 days, very close to one full turn of three stages.

Conclusions

The statistical measurement of trend lengths conducted in this study points to the confirmation of two elements proposed by Hosoda:

• There is a pattern of length whose order of magnitude is adequate, although not completely coincident.
• The basic numbers are more appropriate in bullish than in bearish trends.

It does not seem like Goichi Hosoda established a rigid system in any way, but rather a framework that would focus on relevant issues. This match in some length patterns and in orders of magnitude confirms the importance of the Time element in the evolution of stock asset prices, reasserting the pillars of that area and encouraging a broader use of the complete methodology described by Sasaki in Japanese and Higashino in English.

Similarities found may reaffirm — as a flexible framework — the contributions of Hosoda regarding the temporal element as the basis of price developments, clearing some doubts about its validity and thus encouraging the use of wider and more comprehensive techniques in combining the framework basic charts with Time, Waves and Price projections.

Other researchers are encouraged to study the dispersion of lengths around the mode, and to conduct different research in other markets, assets and timeframes.

References and further reading

• Hidenobu Sasaki (1996), on the basic use of the Ichimoku methodology.
• Yukitoshi Higashino (2014), Primer on Ichimoku, Nippon Technical Analysts Association (NTAA) — how to calculate date reversals using Basic Numbers projections, Time Parity projections or both.
• Thomas Bulkowski (2007), on trend measurement with moving averages.
• Inga Maslova, Harun Onder and Apurva Sanghi (World Bank Working Papers, 2013) and Maharaj and Alonso (2012), on the advantages of wavelet techniques.