Creating the Fractals

The fractal pattern consists of at least five consecutive price bars. An up fractal occurs when the middle bar is the highest among the surrounding bars, while a down fractal is characterized by the middle bar being the lowest. The ideal fractal pattern is visually represented by a V shape for down patterns and an inverted V for up patterns. It's important to note that this pattern has a time bias, as it becomes apparent only after two bars have passed. Consequently, the true completion of the pattern occurs after the fractal signal, typically seen on the middle bar.

Fractals can be highly beneficial when combined with other indicators in various trading strategies. They also serve a role in Elliot Wave analysis by indicating the onset of new waves. The diagram below illustrates this concept further.

According to Elliot Wave theory, the market moves in five impulsive waves followed by three corrective waves. Fractal patterns help signal the conclusion of a specific wave. After a down fractal indicates the end of the first wave, the market gains momentum in the third wave while awaiting confirmation from the down fractal for the decline towards the fifth wave. Here, fractals play a secondary role, as Elliot Wave analysis encompasses more than just this basic approach.

Section 1.1: Coding the Fractal Pattern

Let's explore how to code the fractal pattern using Python. This task is straightforward and involves recursive thinking. The following steps outline the process:

1. The algorithm scans through the data, identifying highs and ensuring that the high from two periods ago is higher than the preceding two highs, forming an inverted V shape.
2. Similarly, for down fractals, it checks for lows that adhere to the same criteria, resulting in a V shape.

Fractals detected on the EURUSD can be generated using the function below:

def fractals(Data, high, low, up, down):

# Fractal Up

for i in range(len(Data)):

if Data[i, high] < Data[i - 2, high] and Data[i - 1, high] < Data[i - 2, high] and Data[i - 2, high] > Data[i - 3, high] and Data[i - 2, high] > Data[i - 4, high]:

Data[i - 2, up] = 1

# Fractal Down

for i in range(len(Data)):

if Data[i, low] > Data[i - 2, low] and Data[i - 1, low] > Data[i - 2, low] and Data[i - 2, low] < Data[i - 3, low] and Data[i - 2, low] < Data[i - 4, low]:

Data[i - 2, down] = -1

return Data

The chart below displays the detected fractals on the hourly values of USDCHF. The upward arrows indicate down fractals, while the downward arrows represent up fractals. Numerous strategies can be developed using these signals, one of which is:

• Buy when a down fractal is confirmed, generating a buy signal two periods after the down fractal appears.
• Sell when an up fractal is confirmed, triggering a sell signal two periods following the up fractal.

Signal chart on the EURUSD:

def signal(Data):

# Bullish Signal

for i in range(len(Data)):

if Data[i - 2, 5] != 0:

Data[i, 6] = 1

# Bearish Signal

for i in range(len(Data)):

if Data[i - 2, 4] != 0:

Data[i, 7] = -1

return Data

The chart below summarizes the signals generated for USDCHF.

Section 1.2: Evaluating the Signals

With the signals established, we can determine when the algorithm would have executed buy and sell orders. This analysis provides a retrospective view of our decisions without hindsight bias. We must assess how the strategy would have performed given our conditions, focusing on return calculations and performance metrics. A key metric to consider is the Signal Quality.

Signal quality evaluates market reactions following a specified period after a signal, essentially measuring market timing. It assumes a fixed holding period and compares market levels at that time to the entry level.

Choosing a Holding Period for a Trend-Following Strategy:

period = 13

def signal_quality(Data, closing, buy, sell, period, where):

Data = adder(Data, 1)

for i in range(len(Data)):

try:

if Data[i, buy] == 1:

Data[i + period, where] = Data[i + period, closing] - Data[i, closing]

if Data[i, sell] == -1:

Data[i + period, where] = Data[i, closing] - Data[i + period, closing]

except IndexError:

pass

return Data

By applying the Signal Quality Function, we can gauge the effectiveness of our strategy.

Am I as disheartened by the fractal patterns as you are? Yes, yet I appreciate that while these fundamental parameters may not yield substantial results, more complex strategies could arise from them. The widespread availability of this pattern in charting software may indicate its limited value.

If you're interested in exploring more technical indicators and strategies, my book may appeal to you.

Always conduct your back-tests. It's essential to question prevailing assumptions; what works for one person may not work for another. My indicators and trading style may be effective for me, but the same may not apply to you.

I advocate for self-learning. Acquiring the idea, function, intuition, and conditions of a strategy allows for personal improvement. My decision not to provide specific back-testing results encourages readers to delve deeper into the strategy and refine it further.