How to correctly calculate Fisher Transform indicator

Question

I'm writing a small technical analysis library that consists of items that are not availabile in TA-lib. I've started with an example I found on cTrader and matched it against the code found in the TradingView version.

Here's the Pine Script code from TradingView:

len = input(9, minval=1, title="Length")

high_ = highest(hl2, len)
low_ = lowest(hl2, len)

round_(val) => val > .99 ? .999 : val < -.99 ? -.999 : val

value = 0.0
value := round_(.66 * ((hl2 - low_) / max(high_ - low_, .001) - .5) + .67 * nz(value[1]))

fish1 = 0.0
fish1 := .5 * log((1 + value) / max(1 - value, .001)) + .5 * nz(fish1[1])

fish2 = fish1[1]

Here's my attempt to implement the indicator:

    public class FisherTransform : IndicatorBase
    {
        public int Length = 9;

        public decimal[] Fish { get; set; }
        public decimal[] Trigger { get; set; }

        decimal _maxHigh;
        decimal _minLow;
 
        private decimal _value1;
        private decimal _lastValue1;

        public FisherTransform(IEnumerable<Candle> candles, int length) 
            : base(candles)
        {
            Length = length;
            RequiredCount = Length;
            _lastValue1 = 1;
        }

        protected override void Initialize()
        {
            Fish = new decimal[Series.Length];
            Trigger = new decimal[Series.Length];
        }

        public override void Compute(int startIndex = 0, int? endIndex = null)
        {
            if (endIndex == null)
                endIndex = Series.Length;

            for (int index = 0; index < endIndex; index++)
            {
                if (index == 1)
                {
                    Fish[index - 1] = 1;
                }
              
                _minLow = Series.Average.Lowest(Length, index);
                _maxHigh = Series.Average.Highest(Length, index);

                _value1 = Maths.Normalize(0.66m * ((Maths.Divide(Series.Average[index] - _minLow, Math.Max(_maxHigh - _minLow, 0.001m)) - 0.5m) + 0.67m * _lastValue1));

                _lastValue1 = _value1;

                Fish[index] = 0.5m * Maths.Log(Maths.Divide(1 + _value1, Math.Max(1 - _value1, .001m))) + 0.5m * Fish[index - 1];
                Trigger[index] = Fish[index - 1];
            }
        }
    }

IndicatorBase class and CandleSeries class

Math Helpers

The problem

The output values appear to be within the expected range however my Fisher Transform cross-overs do not match up with what I am seeing on TradingView's version of the indicator.

Question

How do I properly implement the Fisher Transform indicator in C#? I'd like this to match TradingView's Fisher Transform output.

What I Know

I've check my data against other indicators that I have personally written and indicators from TA-Lib and those indicators pass my unit tests. I've also checked my data against the TradingView data candle by candle and found that my data matches as expected. So I don't suspect my data is the issue.

Specifics

CSV Data - NFLX 5 min agg

Pictured below is the above-shown Fisher Transform code applied to a TradingView chart. My goal is to match this output as close as possible.

Fisher Cyan Trigger Magenta

Expected Outputs:

Crossover completed at 15:30 ET

• Approx Fisher Value is 2.86

• Approx Trigger Value is 1.79

Crossover completed at 10:45 ET

• Approx Fisher Value is -3.67

• Approx Trigger Value is -3.10

My Actual Outputs:

Crossover completed at 15:30 ET

• My Fisher Value is 1.64

• My Trigger Value is 1.99

Crossover completed at 10:45 ET

• My Fisher Value is -1.63

• My Trigger Value is -2.00

Bounty

To make your life easier I'm including a small console application complete with passing and failing unit tests. All unit tests are conducted against the same data set. The passing unit tests are from a tested working Simple Moving Average indicator. The failing unit tests are against the Fisher Transform indicator in question.

Project Files (updated 5/14)

Help get my FisherTransform tests to pass and I'll award the bounty.

Just comment if you need any additional resources or information.

Alternative Answers that I'll consider

• Submit your own working FisherTransform in C#

• Explain why my FisherTransform is actually working as expected

Answer 1

The code has two errors.

1) wrong extra brackets. The correct line is:

_value1 = Maths.Normalize(0.66m * (Maths.Divide(Series.Average[index] - _minLow, Math.Max(_maxHigh - _minLow, 0.001m)) - 0.5m) + 0.67m * _lastValue1);

2) Min and max functions must be:

public static decimal Highest(this decimal[] series, int length, int index)
{
    var maxVal = series[index]; // <----- HERE WAS AN ERROR!

    var lookback = Math.Max(index - length, 0);

    for (int i = index; i-- > lookback;)
        maxVal = Math.Max(series[i], maxVal);

    return maxVal;
}

public static decimal Lowest(this decimal[] series, int length, int index)
{
    var minVal = series[index]; // <----- HERE WAS AN ERROR!

    var lookback = Math.Max(index - length, 0);

    for (int i = index; i-- > lookback;)
    {
        //if (series[i] != 0) // <----- HERE WAS AN ERROR!
            minVal = Math.Min(series[i], minVal);
    }

    return minVal;
}

3) confusing test params. Please recheck your unittest values. AFTER THE UPDATE TESTS STILL NOT FIXED. For an example, the first FisherTransforms_ValuesAreReasonablyClose_First() has mixed values

var fish = result.Fish.Last(); //is equal to -3.1113144510775780365063063706
var trig = result.Trigger.Last(); //is equal to -3.6057793808025449204415435710

// TradingView Values for NFLX 5m chart at 10:45 ET
var fisherValue = -3.67m;
var triggerValue = -3.10m;