Technical Studies Reference

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.

$$ZLEMA_0(X,n) = 0$$

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

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 $$EMA_t(X,n)$$.