chore: import upstream snapshot with attribution
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/*
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* QUANTCONNECT.COM - Democratizing Finance, Empowering Individuals.
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* Lean Algorithmic Trading Engine v2.0. Copyright 2014 QuantConnect Corporation.
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*
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* Licensed under the Apache License, Version 2.0 (the "License");
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* you may not use this file except in compliance with the License.
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* You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0
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*
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* Unless required by applicable law or agreed to in writing, software
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* distributed under the License is distributed on an "AS IS" BASIS,
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* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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* See the License for the specific language governing permissions and
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* limitations under the License.
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*
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*/
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using QuantConnect.Data.Market;
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using System;
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namespace QuantConnect.Indicators
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{
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/// <summary>
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/// The Fisher transform is a mathematical process which is used to convert any data set to a modified
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/// data set whose Probability Distribution Function is approximately Gaussian. Once the Fisher transform
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/// is computed, the transformed data can then be analyzed in terms of it's deviation from the mean.
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///
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/// The equation is y = .5 * ln [ 1 + x / 1 - x ] where
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/// x is the input
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/// y is the output
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/// ln is the natural logarithm
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///
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/// The Fisher transform has much sharper turning points than other indicators such as MACD
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///
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/// For more info, read chapter 1 of Cybernetic Analysis for Stocks and Futures by John F. Ehlers
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///
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/// We are implementing the latest version of this indicator found at Fig. 4 of
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/// http://www.mesasoftware.com/papers/UsingTheFisherTransform.pdf
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/// </summary>
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public class FisherTransform : BarIndicator, IIndicatorWarmUpPeriodProvider
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{
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private const double _alpha = .33;
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private double _previous;
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private readonly Minimum _medianMin;
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private readonly Maximum _medianMax;
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/// <summary>
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/// Initializes a new instance of the FisherTransform class with the default name and period
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/// </summary>
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/// <param name="period">The period of the WMA</param>
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public FisherTransform(int period)
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: this($"FISH({period})", period)
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{
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}
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/// <summary>
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/// A Fisher Transform of Prices
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/// </summary>
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/// <param name="name">string - the name of the indicator</param>
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/// <param name="period">The number of periods for the indicator</param>
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public FisherTransform(string name, int period)
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: base(name)
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{
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// Initialize the local variables
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_medianMax = new Maximum("MedianMax", period);
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_medianMin = new Minimum("MedianMin", period);
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WarmUpPeriod = period;
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}
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/// <summary>
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/// Gets a flag indicating when this indicator is ready and fully initialized
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/// </summary>
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public override bool IsReady => _medianMax.IsReady && _medianMin.IsReady;
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/// <summary>
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/// Required period, in data points, for the indicator to be ready and fully initialized.
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/// </summary>
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public int WarmUpPeriod { get; }
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/// <summary>
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/// Computes the next value in the transform.
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/// value1 is a function used to normalize price withing the last _period day range.
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/// value1 is centered on its midpoint and then doubled so that value1 wil swing between -1 and +1.
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/// value1 is also smoothed with an exponential moving average whose alpha is 0.33.
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///
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/// Since the smoothing may allow value1 to exceed the _period day price range, limits are introduced to
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/// preclude the transform from blowing up by having an input larger than unity.
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/// </summary>
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/// <param name="input">IndicatorDataPoint - the time and value of the next price</param>
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protected override decimal ComputeNextValue(IBaseDataBar input)
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{
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var price = (input.Low + input.High) / 2m;
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_medianMin.Update(input.EndTime, price);
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_medianMax.Update(input.EndTime, price);
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if (!IsReady) return 0;
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var x = 0.0;
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var y = 0.0;
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var minL = _medianMin.Current.Value;
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var maxH = _medianMax.Current.Value;
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if (minL != maxH)
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{
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x = _alpha * 2 * ((double)((price - minL) / (maxH - minL)) - .5) + (1 - _alpha) * _previous;
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y = FisherTransformFunction(x);
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}
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_previous = x;
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return Convert.ToDecimal(y) + .5m * Current.Value;
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}
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/// <summary>
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/// Resets this indicator to its initial state
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/// </summary>
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public override void Reset()
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{
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_previous = 0;
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_medianMax.Reset();
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_medianMin.Reset();
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base.Reset();
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}
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/// <summary>
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/// The Fisher transform is a mathematical process which is used to convert any data set to a modified
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/// data set whose Probability Distribution Function is approximately Gaussian. Once the Fisher transform
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/// is computed, the transformed data can then be analyzed in terms of it's deviation from the mean.
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///
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/// The equation is y = .5 * ln [ 1 + x / 1 - x ] where
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/// x is the input
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/// y is the output
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/// ln is the natural logarithm
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///
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/// The Fisher transform has much sharper turning points than other indicators such as MACD
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///
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/// For more info, read chapter 1 of Cybernetic Analysis for Stocks and Futures by John F. Ehlers
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/// </summary>
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/// <param name="x">Input</param>
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/// <returns>Output</returns>
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private double FisherTransformFunction(double x)
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{
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if (x > .999)
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{
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x = .999;
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}
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if (x < -.999)
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{
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x = -.999;
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}
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return .5 * Math.Log((1.0 + x) / (1.0 - x));
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}
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}
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}
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