QuanTAlib/lib/averages/Jma.cs

using System.Runtime.CompilerServices;
namespace QuanTAlib;

/// <summary>
/// JMA: Jurik Moving Average
/// A sophisticated moving average that combines adaptive volatility measurement with
/// phase-shifted smoothing. JMA provides excellent noise reduction while maintaining
/// responsiveness to significant price movements.
/// </summary>
/// <remarks>
/// The JMA calculation process:
/// 1. Calculates adaptive volatility bands
/// 2. Uses volatility to adjust smoothing parameters
/// 3. Applies phase-shifted smoothing for lag reduction
/// 4. Combines multiple smoothing stages for final output
///
/// Key characteristics:
/// - Adaptive smoothing based on price volatility
/// - Phase-shifting to reduce lag
/// - Excellent noise reduction
/// - Maintains responsiveness to significant moves
/// - Provides volatility bands as additional outputs
///
/// Implementation:
///     Based on known and reverse-engineered insights from Jurik Research
///     Original work by Mark Jurik
/// </remarks>
public class Jma : AbstractBase
{
    private readonly double _period;
    private readonly double _phase;
    private readonly CircularBuffer _vsumBuff;
    private readonly CircularBuffer _avoltyBuff;
    private readonly double _beta;
    private readonly double _len1;
    private readonly double _pow1;
    private readonly double _oneMinusAlpha;
    private readonly double _oneMinusAlphaSquared;
    private readonly double _alphaSquared;

    private double _upperBand, _lowerBand, _p_upperBand, _p_lowerBand;
    private double _prevMa1, _prevDet0, _prevDet1, _prevJma;
    private double _p_prevMa1, _p_prevDet0, _p_prevDet1, _p_prevJma;
    private double _vSum, _p_vSum;

    public double UpperBand { get; set; }
    public double LowerBand { get; set; }
    public double Volty { get; set; }
    public double Factor { get; set; }

    public Jma(int period, int phase = 0, double factor = 0.45, int buffer = 10)
    {
        if (period < 1)
        {
            throw new System.ArgumentOutOfRangeException(nameof(period), "Period must be greater than or equal to 1.");
        }
        Factor = factor;
        _period = period;
        _phase = System.Math.Clamp((phase * 0.01) + 1.5, 0.5, 2.5);

        _vsumBuff = new CircularBuffer(buffer);
        _avoltyBuff = new CircularBuffer(65);
        _beta = factor * (period - 1) / ((factor * (period - 1)) + 2);

        _len1 = System.Math.Max((System.Math.Log(System.Math.Sqrt(period - 1)) / System.Math.Log(2.0)) + 2.0, 0);
        _pow1 = System.Math.Max(_len1 - 2.0, 0.5);

        // Precalculate constants for alpha-based calculations
        double alpha = System.Math.Pow(_beta, _pow1);
        _oneMinusAlpha = 1.0 - alpha;
        _oneMinusAlphaSquared = _oneMinusAlpha * _oneMinusAlpha;
        _alphaSquared = alpha * alpha;

        WarmupPeriod = period * 2;
        Name = $"JMA({period})";
    }

    public Jma(object source, int period, int phase = 0, double factor = 0.45, int buffer = 10) : this(period, phase, factor, buffer)
    {
        var pubEvent = source.GetType().GetEvent("Pub");
        pubEvent?.AddEventHandler(source, new ValueSignal(Sub));
    }

    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public override void Init()
    {
        base.Init();
        _upperBand = _lowerBand = 0.0;
        _p_upperBand = _p_lowerBand = 0.0;
        _avoltyBuff.Clear();
        _vsumBuff.Clear();
    }

    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    protected override void ManageState(bool isNew)
    {
        if (isNew)
        {
            _index++;
            _p_upperBand = _upperBand;
            _p_lowerBand = _lowerBand;
            _p_vSum = _vSum;
            _p_prevMa1 = _prevMa1;
            _p_prevDet0 = _prevDet0;
            _p_prevDet1 = _prevDet1;
            _p_prevJma = _prevJma;
        }
        else
        {
            _upperBand = _p_upperBand;
            _lowerBand = _p_lowerBand;
            _vSum = _p_vSum;
            _prevMa1 = _p_prevMa1;
            _prevDet0 = _p_prevDet0;
            _prevDet1 = _p_prevDet1;
            _prevJma = _p_prevJma;
        }
    }

    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    private double CalculateVolatility(double price, double del1, double del2)
    {
        double volty = System.Math.Max(System.Math.Abs(del1), System.Math.Abs(del2));
        _vsumBuff.Add(volty, Input.IsNew);
        _vSum += (_vsumBuff[^1] - _vsumBuff[0]) / _vsumBuff.Count;
        _avoltyBuff.Add(_vSum, Input.IsNew);
        return volty;
    }

    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    private double CalculateRelativeVolatility(double volty, double avgVolty)
    {
        double rvolty = (avgVolty > 0) ? volty / avgVolty : 1;
        return System.Math.Min(System.Math.Max(rvolty, 1.0), System.Math.Pow(_len1, 1.0 / _pow1));
    }

    protected override double Calculation()
    {
        ManageState(Input.IsNew);

        double price = Input.Value;
        if (_index <= 1)
        {
            _upperBand = _lowerBand = price;
            _prevMa1 = _prevJma = price;
            return price;
        }

        double del1 = price - _upperBand;
        double del2 = price - _lowerBand;
        double volty = CalculateVolatility(price, del1, del2);
        double avgVolty = _avoltyBuff.Average();

        double rvolty = CalculateRelativeVolatility(volty, avgVolty);
        double pow2 = System.Math.Pow(rvolty, _pow1);
        double Kv = System.Math.Pow(_beta, System.Math.Sqrt(pow2));

        _upperBand = (del1 >= 0) ? price : price - (Kv * del1);
        _lowerBand = (del2 <= 0) ? price : price - (Kv * del2);

        double alpha = System.Math.Pow(_beta, pow2);
        double ma1 = price + (alpha * (_prevMa1 - price));
        _prevMa1 = ma1;

        double det0 = price + (_beta * (_prevDet0 - price + ma1)) - ma1;
        _prevDet0 = det0;
        double ma2 = ma1 + (_phase * det0);

        double det1 = ((ma2 - _prevJma) * _oneMinusAlphaSquared) + (_alphaSquared * _prevDet1);
        _prevDet1 = det1;
        double jma = _prevJma + det1;
        _prevJma = jma;

        UpperBand = _upperBand;
        LowerBand = _lowerBand;
        Volty = volty;

        IsHot = _index >= WarmupPeriod;
        return jma;
    }
}