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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.

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.