# Technical Studies Reference

### TRIX

This study calculates and displays the TRIX study.

Let $$X$$ be a random variable denoting the Input Data, and let $$X_t$$ be the value of the Input Data at Index $$t$$. Let the Input Length be denoted as $$n$$. Then we denote the value of TRIX at Index $$t$$ for the given Inputs as $$TRIX_t(X,n)$$, and we compute it using the following sequence of Exponential Moving Averages for the given Inputs.

$$EMA_t^{(1)}(X,n) = EMA_t(X,n)$$
$$EMA_t^{(2)}(X,n) = EMA_t(EMA(X,n),n)$$
$$EMA_t^{(3)}(X,n) = EMA_t(EMA(EMA(X,n),n),n)$$

In the above relations, $$EMA_t^{(j)}$$ denotes the $$j-$$fold composition of the $$EMA$$ function with itself, and $$EMA(X,n)$$ is a random variable denoting the Exponential Moving Average of Length $$n$$ for the Input Data $$X$$. We compute $$TRIX_t(X,n)$$ in terms of these Exponential Moving Averages for $$t \geq 3n - 2$$ as follows.

$$TRIX_t(X,n) = \displaystyle{100 \cdot \frac{EMA_t^{(3)}(X,n) - EMA_{t - 1}^{(3)}(X,n)}{EMA_{t - 1}^{(3)}(X,n)}}$$