# Technical Studies Reference

### Percentage Price Oscillator

This study calculates and displays a Percentage Price Oscillator of the data specified by the Input Data Input.

Let $$X$$ be a random variable denoting the Input Data, and let the Inputs Long Mov Avg Length and Short Mov Avg Length be denoted as $$n_L$$ and $$n_S$$, respectively. Then we denote the Percentage Price Oscillator at Index $$t$$ for the given Inputs as $$PPO_t(X,n_L,n_S)$$, and we compute it for $$t \geq \min\{n_L,n_S\}$$ in terms of Exponential Moving Averages as follows.

$$PPO_t(X,n_L,n_S) = 100\cdot\displaystyle{\left\{ \begin{matrix} \frac{EMA_t(X,n_S) - EMA_t(X,n_L)}{EMA_t(X,n_L)} & EMA_t(X,n_L) \neq 0 \\ PPO_{t - 1}(X,n_L,n_S) & EMA_t(X,n_L) = 0 \end{matrix}\right .}$$

Note: Depending on the setting of the Input Moving Average Type, the Exponential Moving Averages in the above formula could be replaced with Linear Regression Moving Averages, Simple Moving Averages, Weighted Moving Averages, Wilders Moving Averages, Simple Moving Averages - Skip Zeros, or Smoothed Moving Averages.