Invisible Overachiever: Unveiling Fourier Transform

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Dear trading novices and experienced traders, today I am going to introduce to you a "hidden academic leader" in the field of market analysis - the Fisher Transform. This famous indicator was developed by the genius J.F. Ehlers specifically to capture those quiet price reversals.

First, let's take a look at the background of this talented individual. The essence of the Fisher transformation is a clever technique that transforms prices into a Gaussian normal distribution. Does it sound a bit like Gauss himself from math class? That's right, it's the kind of technique that takes a bunch of messy data and makes it neat and tidy, just like the real deal. So, how does the Fisher transformation work? In simple terms, it first converts price data into values between -1 and 1, and then uses a complex mathematical formula (half of the natural logarithm multiplied by some strange thing) to transform this value into another value. It's like turning a wild little rabbit into a tame pet rabbit, doesn't it sound magical? The Fisher transformation formula is as follows: Fisher Transformation = ½ * ln(1 + X / 1 - X);

ln = natural logarithm X = transforming the price from -1 to 1 To calculate the Fisher transformation, first select the review period you want to examine (e.g. nine cycles). This will be the number of periods required for applying this indicator. Once the period is selected, convert the prices within each period into values between -1 and +1. Don't forget to input X and complete all calculations within the formula parentheses. Then multiply the result by the natural logarithm. Multiply the newly obtained result by 0.5. Repeat the calculation process at the end of each period and convert the latest price into a value between -1 and +1 based on the most recent periods.

The superpower of Fisher Hero lies in its ability to help us discover those moments when prices are about to change dramatically. However, like all superheroes, Fisher Transformation also has its own weaknesses. Sometimes, it can give out confusing signals that leave us puzzled. Therefore, the best approach is to combine it with other indicators, such as a trend analysis tool, to more accurately identify buying and selling opportunities.

Now, let's talk about advanced techniques for using Fisher Transformation. When using it, we should pay attention to the various trading signals it generates. However, let's not forget that not all signals are accurate, and there may be false moves at times. Therefore, we need to have a discerning eye to recognize the genuine opportunities. When the curve of Fisher Transformation breaks through its signal line, it's like giving us a little hint, saying, "Hey, buddy, something big might be about to happen!"

In summary, the Fisher Transform is like our market analysis tool that helps us capture those cunning price reversals. Of course, it also requires our intelligence and assistance from other tools to unleash its maximum power. When using the Fisher Transform, remember to stay vigilant and not be deceived by false signals. Let's take a look at the code for the Fisher Transform below:

This piece of code is an implementation of the Fisher Transform indicator. It is written in Pine Script language and is used to plot charts on TradingView.

The following is an explanation of the code:

//@version=5: Specifies the script version as Pine Script 5.

indicator(): Creates an indicator object and sets some properties.

title="Fisher Transform": Sets the indicator title as "Fisher Transform".
shorttitle="Fisher": Sets the short title as "Fisher".
format=format.price: Sets the price formatting option to adapt to the current market's price display method.
precision=2: Sets the decimal point precision to 2 places.
timeframe="": Does not restrict the timeframe (i.e., the indicator can be used on any timeframe).
timeframe_gaps=true: Allows for the presence of time gaps on the chart.

Use the input.int() function to create an integer input variable named len with a default value of 9, a minimum value of 1, and a display name of "Length".

Use the built-in functions tahighest() and talowest() to calculate the highest price and lowest price.

hl2 is a built-in variable that represents the average of the current price (i.e., (high + low) / 2).
len is a previously defined length variable.

Defined a custom function called round_(). It restricts the input value within the range of [-0.999, 0.999] and returns the result.

Initialize a variable named value and calculate a new value using the previously defined round_() function. The formula consists of two parts:

.66 * ((hl2 - low_) / (high_ - low_) - .5) is a part of the Fisher Transform formula.
.67 * nz(value[1]) is a part used to smooth the influence of past data.

Initialize a variable named fish1 and calculate a new value using the Fisher Transform formula. Where:

.5 * math.log((1 + value) / (1 - value)): The second part of the Fisher Transform formula.
.5 * nz(fishl[I]): Smooth the calculation to consider the influence of past data on the current value.

Assign the previous value of fish1 to the variable fish2 for drawing a trigger line.

Use the built-in function hline() to draw a horizontal line. The parameters are as follows:

The first parameter is the position of the horizontal line.
The second parameter is the label displayed in the legend.
Use color= followed by a color code (starting with #) to set the line color.