quantwave_core/indicators/

pma.rs

use crate::indicators::metadata::{IndicatorMetadata, ParamDef};
use crate::traits::Next;
use std::collections::VecDeque;

/// Projected Moving Average (PMA)
///
/// Based on John Ehlers' "Removing Moving Average Lag" (TASC March 2025).
/// Adds the linear regression slope multiplied by half the length to a simple moving average
/// to compensate for the lag inherent in moving averages.
/// Returns (PMA, Predict).
#[derive(Debug, Clone)]
pub struct ProjectedMovingAverage {
    length: usize,
    window: VecDeque<f64>,
    slope_history: VecDeque<f64>,
    sum_x: f64,
    sum_x2: f64,
}

impl ProjectedMovingAverage {
    pub fn new(length: usize) -> Self {
        let mut sum_x = 0.0;
        let mut sum_x2 = 0.0;
        for i in 1..=length {
            let x = i as f64;
            sum_x += x;
            sum_x2 += x * x;
        }
        Self {
            length,
            window: VecDeque::with_capacity(length),
            slope_history: VecDeque::from(vec![0.0; 3]),
            sum_x,
            sum_x2,
        }
    }
}

impl Default for ProjectedMovingAverage {
    fn default() -> Self {
        Self::new(20)
    }
}

impl Next<f64> for ProjectedMovingAverage {
    type Output = (f64, f64);

    fn next(&mut self, input: f64) -> Self::Output {
        self.window.push_front(input);
        if self.window.len() > self.length {
            self.window.pop_back();
        }

        if self.window.len() < self.length {
            return (input, input);
        }

        let mut sum_y = 0.0;
        let mut sum_xy = 0.0;

        for i in 0..self.length {
            let y = self.window[i];
            let x = (i + 1) as f64;
            sum_y += y;
            sum_xy += x * y;
        }

        let n = self.length as f64;
        let denom = n * self.sum_x2 - self.sum_x * self.sum_x;
        let slope = if denom != 0.0 {
            -(n * sum_xy - self.sum_x * sum_y) / denom
        } else {
            0.0
        };
        let sma = sum_y / n;
        let pma = sma + slope * n / 2.0;

        self.slope_history.pop_back();
        self.slope_history.push_front(slope);

        let predict = pma + 0.5 * (slope - self.slope_history[2]) * n;

        (pma, predict)
    }
}

pub const PROJECTED_MOVING_AVERAGE_METADATA: IndicatorMetadata = IndicatorMetadata {
    name: "Projected Moving Average",
    description: "A lag-compensated moving average that uses linear regression slope to project the average forward.",
    usage: "Use as a predictive moving average that uses linear regression projection to anticipate where price will be rather than where it has been, reducing effective lag.",
    keywords: &["moving-average", "prediction", "ehlers", "zero-lag"],
    ehlers_summary: "The Projected Moving Average uses linear regression over the lookback window to project the best-fit line forward to the current bar. This predictive approach shifts the MA output toward the leading edge of price movement, achieving reduced lag compared to conventional MAs of the same period.",
    params: &[ParamDef {
        name: "length",
        default: "20",
        description: "Calculation length",
    }],
    formula_source: "https://github.com/lavs9/quantwave/blob/main/references/traderstipsreference/TRADERS’%20TIPS%20-%20MARCH%202025.html",
    formula_latex: r#"
\[
Slope = -\frac{n \sum xy - \sum x \sum y}{n \sum x^2 - (\sum x)^2}
\]
\[
PMA = SMA + Slope \cdot \frac{n}{2}
\]
\[
Predict = PMA + 0.5 \cdot (Slope - Slope_{t-2}) \cdot n
\]
"#,
    gold_standard_file: "pma.json",
    category: "Ehlers DSP",
};

#[cfg(test)]
mod tests {
    use super::*;
    use crate::traits::Next;
    use proptest::prelude::*;

    #[test]
    fn test_pma_basic() {
        let mut pma = ProjectedMovingAverage::new(20);
        let inputs = vec![10.0; 40];
        for input in inputs {
            let (p, pr) = pma.next(input);
            assert_eq!(p, 10.0);
            assert_eq!(pr, 10.0);
        }
    }

    proptest! {
        #[test]
        fn test_pma_parity(
            inputs in prop::collection::vec(1.0..100.0, 40..100),
        ) {
            let length = 20;
            let mut pma = ProjectedMovingAverage::new(length);
            let streaming_results: Vec<(f64, f64)> = inputs.iter().map(|&x| pma.next(x)).collect();

            // Batch implementation
            let mut batch_results = Vec::with_capacity(inputs.len());
            let mut slope_hist = vec![0.0; 3];
            let mut sum_x = 0.0;
            let mut sum_x2 = 0.0;
            for i in 1..=length {
                let x = i as f64;
                sum_x += x;
                sum_x2 += x * x;
            }

            for i in 0..inputs.len() {
                if i < length - 1 {
                    batch_results.push((inputs[i], inputs[i]));
                    continue;
                }

                let mut sum_y = 0.0;
                let mut sum_xy = 0.0;
                for j in 0..length {
                    let y = inputs[i - j];
                    let x = (j + 1) as f64;
                    sum_y += y;
                    sum_xy += x * y;
                }

                let n = length as f64;
                let denom = n * sum_x2 - sum_x * sum_x;
                let slope = if denom != 0.0 {
                    -(n * sum_xy - sum_x * sum_y) / denom
                } else {
                    0.0
                };
                let sma = sum_y / n;
                let pma_val = sma + slope * n / 2.0;

                slope_hist.insert(0, slope);
                if slope_hist.len() > 3 {
                    slope_hist.pop();
                }

                let predict = pma_val + 0.5 * (slope - slope_hist[2]) * n;
                batch_results.push((pma_val, predict));
            }

            for (s, b) in streaming_results.iter().zip(batch_results.iter()) {
                approx::assert_relative_eq!(s.0, b.0, epsilon = 1e-10);
                approx::assert_relative_eq!(s.1, b.1, epsilon = 1e-10);
            }
        }
    }
}