Ehlers Autocorrelation Periodogram (ACP)

Category: cycle

An advanced cycle estimator that uses autocorrelation and a modified Discrete Fourier Transform to extract the dominant market cycle and its power.

Formula

\begin{aligned} &\text{1. High-Pass Filter (HP):} \\ &HP_t = (1-\frac{\alpha}{2})^2(x_t - 2x_{t-1} + x_{t-2}) + 2(1-\alpha)HP_{t-1} - (1-\alpha)^2HP_{t-2} \\ &\text{2. Pearson Correlation for each lag } L: \\ &r_L = \frac{n\sum xy - \sum x \sum y}{\sqrt{(n\sum x^2 - (\sum x)^2)(n\sum y^2 - (\sum y)^2)}} \\ &\text{3. Periodogram Power for Period } T: \\ &P(T) = \left(\sum_{n=2}^{max} r_n \cos(\frac{2\pi n}{T})\right)^2 + \left(\sum_{n=2}^{max} r_n \sin(\frac{2\pi n}{T})\right)^2 \\ &\text{4. Dominant Cycle (DC):} \\ &DC = \frac{\sum_{T=min}^{max} T \cdot P(T)^3}{\sum_{T=min}^{max} P(T)^3} \text{ (where } P(T) \ge 0.5\text{)} \end{aligned}

Inputs

• Source (default: close)
• Min Period (default: 8)
• Max Period (default: 48)
• Autocorrelation Length (avgLength) (default: 3)
• Enhance Resolution (Cubic emphasis) (default: true)

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