Reverse EMA
A causal forward and backward EMA indicator that minimizes lag using a series of alignment filters.
Usage
Use to identify trends or cycles with minimal lag. Higher alpha values (e.g., 0.3) isolate cycles, while lower values (e.g., 0.05) isolate trends.
Background
Ehlers' Reverse EMA approximates a non-causal zero-lag filter by using a product series of Z-transform components. It achieves double smoothing at high frequencies and mitigates spectral dilation at low frequencies, providing a unique balance of smoothness and responsiveness.
Parameters
alpha(default: 0.1): Smoothing factor (0.0 to 1.0)
Formula
[ EMA = \alpha \cdot Price + (1 - \alpha) \cdot EMA_{t-1} ] [ RE_1 = (1 - \alpha) \cdot EMA + EMA_{t-1} ] [ RE_i = (1 - \alpha)^{2^{i-1}} \cdot RE_{i-1} + RE_{i-1, t-1} \text{ for } i=2..8 ] [ Wave = EMA - \alpha \cdot RE_8 ]