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Technical Studies Reference

Moving Average - Smoothed

This study calculates and displays a smoothed moving average of the data specified by the Input Data Input.

Let $$X$$ be a random variable denoting the Input Data, and let $$X_i$$ be the value of the Input Data at Index $$i$$. Let the Length Input be denoted as $$n$$. Then we denote the Moving Average - Smoothed at Index $$t$$ for the given Inputs as $$SMMA_t(X,n)$$, and we compute it for $$t \geq n - 1$$ as follows.

$$\displaystyle{SMMA_t(X,n) = \left\{\begin{matrix} SMA_{n - 1}(X,n) & t = n - 1 \\ \frac{n\cdot SMMA_{t - 1}(X,n) - SMMA_{t - 1}(X,n) + X_t}{n} & t > n - 1 \end{matrix}\right .}$$

In the above formula, $$SMA_{n - 1}(X,n)$$ denotes the Simple Moving Average at $$t = n - 1$$.