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### Moving Average - Zero Lag Exponential

This study calculates a zero lag exponential moving average of the data specified by the **Input Data** Input.

Let \(X\) be a random variable denoting the **Input Data**, and let \(X_t\) be the value of the **Input Data** at chart bar \(t\). Let the Input **Zero Lag EMA Length** be denoted as \(n\). Then we denote the **Moving Average - Zero Lag Exponential** at chart bar \(t\) for the given Inputs as \(ZLEMA_t(X,n)\), and we compute it using the following recursion relation.

\(ZLEMA_t(X,n) = c\left(2X_t - X_{t - L}\right) + (1 - c)ZLEMA{t-1}(X,n)\)

The constant \(L\) is called the Lag, and it is computed as follows.

\(L = \left\lceil{\frac{n-1}{2}}\right\rceil\)For an explanation of the ceiling function (\(\left\lceil{\space\space}\right\rceil\)), refer to the Wikipedia article Floor and ceiling functions.

The constant \(c\) is the same multiplier that is found in the Exponential Moving Average.

If \(L = 0\), then \(ZLEMA_t(X,n)\) becomes identical to \(EMA_t(X,n)\).

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*Last modified Friday, 09th June, 2017.