With Time Fractals
A special Report by Walter Bressert
Time and price cycles in the futures markets and stocks "exhibit patterns in time and space that are orderly and self-similar in scale", (1) or fractal. To get a rough mental picture of fractals, draw a triangle with three equal sides. Divide each side into three equal parts and build another triangle on the outside of the middle one third of each side. The result is the Star of David. Now repeat this process on each of the new triangles, and then each of the newer triangles, and each of the newer triangles, and on and on and on. The resulting form is composed of smaller and smaller triangles of the exact same design and proportion as the original triangle. This is called a Koch Snowflake.
I first read James Gleick's book "Chaos" more than 10 years ago. As a futures trader looking for an edge to trade and forecast the markets, I was fascinated by the similarities in my research on cycles and technical analysis in the futures markets with chaos and fractals. In the Koch snowflake each smaller triangle has the same proportion as the larger triangle. Time cycles in the markets are linear and each proportionate time frame has a dominant trading cycle of approximately the same length. Could proportionally smaller time frames, which I call "time fractals", reveal meaningful market patterns in the way that fractals reveal the similarity of seemingly random objects of nature? At the time I was basing my analysis and trading mainly on cycles in daily and weekly charts. "Chaos" gave me a new perspective. In 1994 my research expanded to include multiple intra-day time frames in the futures markets.
Benefits of Trading with Time Fractals
Fractals and Trading Cycles
Combinations that Identify Trading Cycle Tops and Bottoms
Charts 2 and 3 illustrate the use of the RSI3M3 oscillator and the buy signals in the 200 and 50-minute time frames.
oscillator. This is called detrending. The result is the green detrended RSI3M3 plotted below it. A buy signal for this more sensitive oscillator is constructed using the same pattern of a drop below the buy line, upturn and setup bar. The combination of the RSI3M3 and the 3M3detrend generated buy signals (at the red dots) following three of the four trading cycle bottoms, and several of the half-cycle bottoms.
on Timing Bands
High Probability Buy Signals
drop into a 38-62% retracement,
Fractals in the TBOND Market
Each of these time fractals has a cycle length of approximately the same number of bars as the 20-day trading cycle. The time lengths for the price bars are proportionate to the full 400-minute trading session - 200-minutes, 50-minutes, 25-minutes. Using these time proportions in the Bond market is important because when a longer cycle bottoms the shorter cycles bottom at the same time. Going back to the Koch snowflake, smaller triangles on the sides of a larger one lead to a point where the apex of smaller triangles fits snuggly into the apex of the larger. Often, shorter cycles will contract or extend to coincide with the bottom of the larger, more powerful cycles. Knowing a daily cycle is bottoming means a "nest" of all shorter fractal cycles are also bottoming.
Most importantly, the dominant longer-term cycle sets the trend for the shorter intra-day cycle(s). In the trendy TBond market, the 200-minute chart sets the trend for intra-day trading. Knowing the cycle bottoms will "nest", or bottom at the same time as the largest cycle can offer low dollar risk trades at bottoms of the 20-bar trading cycle of the 200-minute chart. And once this cycle has bottomed, knowing the trend allows you to buy bottoms in an uptrend (or sell cycle tops in a downtrend), which is the safest way to trade.
Combining Mechanical Signals with Forecasts of Cycle Tops & Bottoms
Chart #1 - Daily or 400-Minute Chart The red dots are mechanical buy entry signals generated by the RSI3M3 illustrated earlier. Notice that each of the buy signals occurs following a bottom of the 20-day cycle. The timing bands to forecast the cycle tops and bottoms have been left off this chart to cut down on "chart clutter".
Chart #2 - The 200-Minute Chart
Chart #3 - 50-Minute Chart
The trading cycle bottom at A begins a trading cycle in the 200-minute bar chart which ends at X. This cycle is also the half-cycle in Chart #1 at X. This 50-minute chart further illustrates the fractal structure of Tbonds as each of the trading cycles in the 50-minute chart, labeled 1, 2, 3 and 4, average 20-bars from bottom to bottom. This is the same cycle length as in the daily, 200-minute and 100-minute charts. Each trading cycle in the 200-minute bar chart contains an average of four trading cycles in the 50-minute chart; each trading cycle in the daily chart, or 400-minute chart, averages eight trading cycles of the 50-minute chart.
Chart #4 - 25-Minute Bar Chart
With price bars one-half of those in the 50-minute bar chart, each 20-bar trading cycle in this time period is a 10-bar half-cycle in the 50-minute bar chart. · The daily trading cycle and the trading cycle in the 200 minute chart bottomed at A. · The blue numbers, 1 through 4 are the cycle bottoms of the 20 bar cycle in the 50 minute bar chart. · The 25-minute 20-bar trading cycle bottoms are at A, 1a, 1b, 2a, 2b, 3a, 3b, 4a and 4b. Each of these cycles is a half-cycle of the 20-bar trading cycle in the 50-minute bar chart.
Trend with Time Fractals
Timing Bands & Fibonacci Retracements to Find the Next Buy Zone
THE S&P; INDEX WITH 20-MINUTE AND 5-MINUTE PRICE BARS
Fractals Reduce Risk:
The trading time frame in the S&P; Index is the 5-minute bar chart, one-fourth of the 20-minute chart. Short-term money trades this time frame aggressively. The 22-bar trading cycle in this 5-minute bar chart has eight trading cycle bottoms. Using the 5-minute bar chart to trade trend reversals of the 18-bar cycle in the 20-minute chart greatly reduces the dollar risk of trying to catch the trend reversal using the 20-minute chart alone. At all three bottoms the dollar risk from entry to protective stop on the 5-minute is less than half of the dollar risk incurred trading the buy signals on the 20-minute chart. Even better, the odds of buying a cycle bottom are much greater.
In this 5-minute chart the eight trading cycle bottoms are indicated by the arrows and numbered 1 through 8. The timing bands for the significant cycles are plotted along the bottom of the chart. The blue band is the time period in which the top is most likely to occur; the red band is the time period in which the bottom of the 22-bar cycle is most likely to occur. Higher probabilities for trend reversals occur when the timing band for the cycle bottom in the 5-minute bar chart coincides with the bottoming timing band for the trading cycle in the 20-minute bar chart.
When prices drop into a red bottoming timing band for an 11 and 22-bar cycle bottom, and a buy signal is generated, the historical odds of the signal identifying the trading cycle bottom are 80%+. That means the odds are over 80% that prices will move to the top of at least an 11-bar cycle, and possibly a 22-bar cycle, before moving lower.
Borrowing the Koch snowflake again, the apex of larger triangles coincides with the apex of smaller ones in the same way that cycles of various time fractals bottom simultaneously with the larger trading cycle. Prior to the apex of larger triangles are the peaks and troughs of several smaller ones, located on the side of larger triangle. Several cycle bottoms in the 5-minute chart are possible before getting to a cycle bottom in the 20-minute, which will most likely occur in the red timing band. A bottom in the 5-minute chart coinciding with 20-minute prices in a red timing band gives us a strong likelihood that the larger trading cycle is bottoming also.
the Odds with Fibonacci Retracements
There was no buy signal generated at Trading Cycle 3, 4 or 6 using the RSI3M3. Other oscillators, however, would have generated buy signals that could have been taken. Following the bottom at 6, prices rose to test the earlier high (made following the bottom of cycle 3) then dropped below the trading cycle bottom at 6. This was the first time since the bottom at B that prices dropped below a trading cycle low on the 5-minute bar chart. This indicated the cycle in the 20-minute bar chart had topped. No new long positions would be taken until the cycle in the 20-minute bar chart bottoms at C. At C, Trading Cycle 8, prices bottomed in the red timing band for both the 5-minute bar chart and the 20-minute bar chart. The buy signal that followed this bottom gave 80%+ odds of a trading cycle bottom having occurred in a 5-minute bar chart, which was confirmed by the buy signal in the 20-minute bar chart.
BENEFITS OF TRADING WITH INTRA-DAY TIME FRACTALS
CHAOS James Gleick, Making a New Science (New York: Penguin Books USA, 1987) (1) page 308 (2) page 99
My thanks to Doug Schaff who revised and edited the original report. WB
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