QuanTAlib/Source/Trends/JMA_Series.cs

namespace QuanTAlib;
using System;
using System.Linq;

/* <summary>
JMA: Jurik Moving Average
    Mark Jurik's Moving Average (JMA) attempts to eliminate noise to see the
    underlying activity. It has extremely low lag, is very smooth and is responsive
    to market gaps.

Sources:
    https://c.mql5.com/forextsd/forum/164/jurik_1.pdf
    https://www.prorealcode.com/prorealtime-indicators/jurik-volatility-bands/

Issues:
    Real JMA algorithm is not published and this formula is derived through
    deduction and reverse analysis of JMA behavior. It is really close, but not
    exact - published JMA tests against JMA.CSV fail with small deviation. The
    original algo is slightly different, yet this approximation is close enough.

</summary> 
*/
public class JMA_Series : Single_TSeries_Indicator {
	private readonly System.Collections.Generic.List<double> volty_10 = new();
	private readonly System.Collections.Generic.List<double> vsum_buff = new();
	private readonly double pr;
	public TSeries mma1 { get; }
	public TSeries mma2 { get; }

	private double upperBand, lowerBand, vsum, Kv, del1, del2;
	private double prev_ma1, prev_det0, prev_det1, prev_vsum, prev_jma;
	private double p_upperBand, p_lowerBand, p_Kv, p_prev_ma1, p_prev_det0, p_prev_det1, p_prev_vsum, p_prev_jma;

	public JMA_Series(TSeries source, int period, double phase = 0.0, bool useNaN = false) : base(source, period, useNaN) {
		upperBand = lowerBand = prev_ma1 = prev_det0 = prev_det1 = prev_vsum = prev_jma = Kv = del1 = del2 = 0.0;
		Kv = 0;
		pr = (phase * 0.01) + 1.5;
		if (phase < -100) pr = 0.5;
		if (phase > 100) pr = 2.5;

		mma1 = new();
		mma2 = new();

		if (base._data.Count > 0) { base.Add(base._data); }
	}

	public override void Add((System.DateTime t, double v) TValue, bool update) {
		if (this.Count == 0) { prev_ma1 = TValue.v; }
		if (update) {
			upperBand = p_upperBand;
			lowerBand = p_lowerBand;
			Kv = p_Kv;
			prev_vsum = p_prev_vsum;
			prev_ma1 = p_prev_ma1;
			prev_det0 = p_prev_det0;
			prev_det1 = p_prev_det1;
			prev_jma = p_prev_jma;
		}
		else {
			p_upperBand = upperBand;
			p_lowerBand = lowerBand;
			p_Kv = Kv;
			p_prev_vsum = prev_vsum;
			p_prev_ma1 = prev_ma1;
			p_prev_det0 = prev_det0;
			p_prev_det1 = prev_det1;
			p_prev_jma = prev_jma;
		}

		// from Tvalue to volty
		del1 = TValue.v - upperBand;
		del2 = TValue.v - lowerBand;
		upperBand = (del1 > 0) ? TValue.v : TValue.v - (Kv * del1);
		lowerBand = (del2 < 0) ? TValue.v : TValue.v - (Kv * del2);
		double volty = 0;
		if (Math.Abs(del1) > Math.Abs(del2)) { volty = Math.Abs(del1); }
		if (Math.Abs(del1) < Math.Abs(del2)) { volty = Math.Abs(del2); }

		//// from volty to avolty
		if (update) { volty_10[volty_10.Count - 1] = volty; }
		else { volty_10.Add(volty); }
		if (volty_10.Count > _p) { volty_10.RemoveAt(0); }
		vsum = prev_vsum + 0.1 * (volty - volty_10.First());
		if (update) { vsum_buff[vsum_buff.Count - 1] = vsum; }
		else { vsum_buff.Add(vsum); }
		if (vsum_buff.Count > (65))
			vsum_buff.RemoveAt(0);
		double avolty = 0;
		for (int i = 0; i < vsum_buff.Count; i++) { avolty += vsum_buff[i]; }
		avolty /= vsum_buff.Count;

		/// from avolty to rolty
		double rvolty = (avolty != 0) ? volty / avolty : 0;
		double len1 = (Math.Log(Math.Sqrt(0.5 * (_p - 1))) / Math.Log(2.0)) + 2;
		if (len1 < 0)
			len1 = 0;
		double pow1 = Math.Max(len1 - 2.0, 0.5);
		if (rvolty > Math.Pow(len1, 1.0 / pow1))
			rvolty = Math.Pow(len1, 1.0 / pow1);
		if (rvolty < 1)
			rvolty = 1;

		//// from rvolty to second smoothing
		double pow2 = Math.Pow(rvolty, pow1);
		double len2 = Math.Sqrt(0.5 * (_p - 1)) * len1;
		Kv = Math.Pow(len2 / (len2 + 2), Math.Sqrt(pow2));
		double beta = 0.45 * (_p - 1) / (0.45 * (_p - 1) + 2);
		double alpha = Math.Pow(beta * 1.1, pow2);
		double ma1 = (1 - alpha) * TValue.v + alpha * prev_ma1;
		prev_ma1 = ma1;
		mma1.Add(ma1);

		double det0 = (1 - beta) * (TValue.v - ma1) + beta * prev_det0;
		prev_det0 = det0;
		double ma2 = ma1 + pr * det0;
		mma2.Add(ma2);

		double det1 = ((1 - alpha) * (1 - alpha) * (ma2 - prev_jma)) + (alpha * alpha * prev_det1);
		prev_det1 = det1;
		double jma = prev_jma + det1;
		prev_jma = jma;

		base.Add((TValue.t, ma1), update, _NaN);
	}
}