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# Moving Average - Variable Index Dynamic

This study calculates and displays a Variable Index Dynamic Moving Average of the data specified by the **Input Data** Input. This study was developed by Tushar S. Chande, Ph.D., in his article *Adapting Moving Averages to Market Volatility*, which was published in Stocks & Commodities V. 10:3 (pp 108-114). The closely related studies Rapid Adaptive Variance Indicator and Turbo MACD were presented in the same article.

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 Inputs **VIDYA Length**, **Std Dev Length**, **Reference Standard Deviation**, and **Percentage Offset** be denoted as \(n_V\), \(n_{\sigma}\), \(\sigma_{ref}\), and \(k\), respectively. Then we denote the **Moving Average - Variable Index Dynamic** at Index \(t\) for the given Inputs as \(VIDYA_t(X,n_V, n_{\sigma}, \sigma_{ref})\), and we compute it in terms of the Standard Deviation as follows.

For \(0 \leq t < n_{\sigma} - 2\):

\(\displaystyle{VIDYA_t(X,n_V, n_{\sigma}, \sigma_{ref}) = 0}\)For \(t \geq n_{\sigma} - 2\):

\(\displaystyle{VIDYA_t(X,n_V, n_{\sigma}, \sigma_{ref}) = \frac{2}{n_V + 1} \cdot \frac{\sigma_t(X,n_{\sigma})}{\sigma_{ref}} \cdot X_t + \left(1 - \frac{2}{n_V + 1}\right) \cdot VIDYA_{t - 1}(X,n_V, n_{\sigma}, \sigma_{ref}, k)}\)This study displays two other Subgraphs, namely the Top VIDYA Band and Bottom VIDYA Band, denoted respectively as \(TB_t^{(VIDYA)}(X,n_V, n_{\sigma}, \sigma_{ref}, k)\) and \(BB_t^{(VIDYA)}(X,n_V, n_{\sigma}, \sigma_{ref}, k)\). We compute them as follows.

\(\displaystyle{TB_t^{(VIDYA)}(X,n_V, n_{\sigma}, \sigma_{ref}, k) = VIDYA_t(X,n_V, n_{\sigma}, \sigma_{ref}) + \frac{k}{100} \cdot VIDYA_t(X,n_V, n_{\sigma}, \sigma_{ref})}\)\(\displaystyle{BB_t^{(VIDYA)}(X,n_V, n_{\sigma}, \sigma_{ref}, k) = VIDYA_t(X,n_V, n_{\sigma}, \sigma_{ref}) - \frac{k}{100} \cdot VIDYA_t(X,n_V, n_{\sigma}, \sigma_{ref})}\)

#### Inputs

- Input Data
- VIDYA Length
- Std Dev Length
**Reference Standard Deviation**: A scaling divisor. The volatility of the**Input Data**is measured as a number of Reference Standard Deviations.- Percentage Offset

#### 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 Tuesday, 27th September, 2022.