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### Adaptive RSI Moving Average with Smoothing

This study calculates a type of adaptive moving average of the data specified by the **Input Data**. Unlike the Adaptive Moving Average, this study incorporates the Relative Strength Index (RSI) of the **Input Data**. The study allows for optional smoothing of both the **Input Data** and the RSI.

__Smoothed vs Unsmoothed Input Data__Let \(X\) be a random variable denoting the **Input Data**, and let \(X_t\) be the value of the **Input Data** at chart bar \(t\). If the value of the **Set Price Smoothing?** Input is No, then the unsmoothed **Input Data** \(X\) is used in the subsequent calculations. If the value is Yes (default value), then the smoothed **Input Data** is used instead. The smoothing is done with an Exponential Moving Average whose **Length** is given by the **Price Smoothing Period** Input, denoted as \(n_{PS}\).

We define a new random variable \(P\) denoting the Price (smoothed or unsmoothed). We denote the value of \(P\) at chart bar \(t\) as \(P_t\), and we compute it as follows.

\(P_t =\left\{ \begin{matrix} X_t & Price \space Smoothing = No \\ EMA_t\left(X,n_{PS}\right) & Price \space Smoothing = Yes \end{matrix}\right .\)**Note**: Depending on the setting of the Input **Price Smoothing Average Type**, the Exponential Moving Average in the calculation of the smoothed **Input Data** 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.

__Smoothed vs Unsmoothed RSI__The RSI is calculated for \(P\) with **Length** given by the **ARSI Period**, denoted as \(n_{ARSI}\). The type of Moving Average used in the calculation of the RSI is determined by the **ARSI Moving Average Type** Input. If the value of the **Set RSI Smoothing?** Input is No, then the RSI at chart bar \(t\) is given by \(RSI_t\left(P,n_{ARSI}\right)\). If the value is Yes (default value), then the smoothed RSI is used instead. The smoothing is done with an Exponential Moving Average whose **Length** is given by the **RSI Smoothing Period** Input, denoted as \(n_{RSIS}\).

We define a new random variable \(R\) denoting the RSI (smoothed or unsmoothed). We denote the value of \(R\) at chart bar \(t\) as \(R_t\), and we compute it as follows.

\(R_t =\left\{ \begin{matrix} RSI_t\left(P,n_{ARSI}\right) & RSI \space Smoothing = No \\ EMA_t\left(RSI\left(P,n_{ARSI}\right)\right) & RSI \space Smoothing = Yes \end{matrix}\right .\)**Note**: Depending on the setting of the Input **RSI Smoothing Average Type**, the Exponential Moving Average in the calculation of the smoothed **Input Data** 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.

__Scaling Factor__Let \(SF\) be a random variable denoting the Scaling Factor, and let \(s\) denote the **ARSI Scale Factor** Input. We denote the value of \(SF\) at chart bar \(t\) as \(SF_t\), and we compute it as follows.

__Adaptive RSI Moving Average__

The **Adaptive RSI Moving Average** at chart bar \(t\) for Price \(P\) and Scaling Factor \(SF\) is denoted as \(ARSIMA_t(P,SF)\), and we compute it with the following recursion relation.

\(ARSIMA_t(P,SF) = \left(P_t - ARSIMA_{t - 1}(P,SF)\right)SF_t + ARSIMA_{t - 1}(P,SF)\)

#### Inputs

- ARSI Period
- ARSI Moving Average Type
- Input Data
**Set Price Smoothing?**: This Input determines whether or not the**Input Data**is to be smoothed by taking a Moving Average.- Price Smoothing Period
- Price Smoothing Moving Average Type
**Set RSI Smoothing?**: This Input determines whether or not the RSI is to be smoothed by taking a Moving Average.- RSI Smoothing Period
- RSI Smoothing Moving Average Type
**ARSI Scale Factor**: This Input determines the amplitude of the Scaling Factor.

*Last modified Friday, 09th June, 2017.