# Technical Studies Reference

### Moving Average - Triangular

This study calculates and displays a Triangular Moving Average of the data specified by the Input Data Input. The Triangular Moving Average is calculated in terms of the Simple Moving Average. Refer to that study to familiarize yourself with the notation used here.

Just as with the Simple Moving Average, this study relies on the Inputs Data Input $$X$$ and Length $$n$$. We calculate two additional Lengths based on $$n$$, $$n_1(n)$$ and $$n_2(n)$$, as follows.

$$\displaystyle{n_1(n) =\left\{ \begin{matrix} \left\lceil{\frac{n}{2}}\right\rceil & n \space odd\\ \frac{n}{2} & n \space even \end{matrix}\right .}$$

$$\displaystyle{n_2(n) =\left\{ \begin{matrix} \left\lceil{\frac{n}{2}}\right\rceil & n \space odd\\ n_1 + 1 & n \space even \end{matrix}\right .}$$

For an explanation of the ceiling function ($$\left\lceil{\space\space}\right\rceil$$), refer to our description here.

We denote the Moving Average - Triangular at Index $$t$$ for the given Input Data and calculated Lengths as $$TMA_t(X,n)$$, and we compute it for $$t \geq n_1(n) + n_2(n) - 1$$ as follows.

$$TMA_t(X,n) = MA_t\left(MA\left(X,n_1(n)\right),n_2(n)\right)$$ In the above formula, $$MA\left(X,n_1(n)\right)$$ is a random variable denoting the Simple Moving Average of Length $$n_1(n)$$ for the Input Data $$X$$.