# Technical Studies Reference

### 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.

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