Zero lag exponential moving average

The zero lag exponential moving average (ZLEMA) is a technical indicator within technical analysis that aims is to eliminate the inherent lag associated to all trend following indicators which average a price over time. As is the case with the double exponential moving average (DEMA) and the triple exponential moving average (TEMA) this indicator aims to reduce the lag.

History

The indicator was created by John Ehlers and Ric Way around 2010.

Formula

The formula for a given N-Day period and for a given data series is:

$\begin{array}{cc}\mathit{\text{𝐿𝑎𝑔}}& =\frac{Period-1}{2}\\ \mathit{\text{𝐸𝑚𝑎𝐷𝑎𝑡𝑎}}& =\mathit{\text{𝐷𝑎𝑡𝑎}}+(\mathit{\text{𝐷𝑎𝑡𝑎}}-\mathit{\text{𝐷𝑎𝑡𝑎}}(\text{Lag days ago}))\\ \mathit{\text{𝑍𝐿𝐸𝑀𝐴}}& =\mathit{\text{𝐸𝑀𝐴}}(\mathit{\text{𝐸𝑚𝑎𝐷𝑎𝑡𝑎}},\mathit{\text{𝑃𝑒𝑟𝑖𝑜𝑑}})\end{array}$

The idea is do a regular exponential moving average (EMA) calculation but on a de-lagged data instead of doing it on the regular data. Data is de-lagged by removing the data from "lag" days ago thus removing (or attempting to) the cumulative effect of the moving average.