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### Price Momentum Oscillator

This study calculates and displays a Price Momentum Oscillator and its Moving Average for the data specified by the **Input Data** Input.

Let \(X\) be a random variable denoting the **Input Data**, and let \(X_t\) denote the value of \(X\) at Index \(t\). The first step is to calculate the Rate of Change for \(t \geq 1\) as follows.

Next we define a Custom Smoothing Function \(CSF_t(X,n)\) as follows.

\(\displaystyle{CSF_t(X,n) = \left\{ \begin{matrix} X_1 & t = 1 \\ \frac{2}{n}\cdot (X_t - CSF_{t - 1}(X,n)) + CSF_{t - 1}(X,n)) & t > 1 \end{matrix}\right .}\)Let the **PMO Line Length 1**, **PMO Line Length 2**, and **PMO Signal Line Length** Inputs be denoted as \(n_1\), \(n_2\), and \(n_{Sig}\), respectively. We denote the Smoothed ROC at Index \(t\) as \(\overline{ROC}_t(X,1,100,n_1)\), and we compute it for \(t \geq 1\) as follows.

We denote the **Price Momentum Oscillator** Line at Index \(t\) as \(PMO_t(X,n_1,n_2)\), and we compute it for \(t \geq 1\) as follows.

We denote the **Price Momentum Oscillator** Signal Line as \(\overline{PMO}_t(X,n_1,n_1,n_{Sig})\), and we calculate it for \(t \geq 1\) in terms of an Exponential Moving Average as follows.

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

#### Inputs

#### Spreadsheet

The spreadsheet below contains the formulas for this study in Spreadsheet format. Save this Spreadsheet to the Data Files Folder.

Open it through **File >> Open Spreadsheet**.

*Last modified Friday, 08th March, 2019.