# Technical Studies Reference

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### Turbo MACD

This study calculates and displays a Turbo MACD (TMACD) 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 Variable Index Dynamic Moving Average (VIDYA) and Rapid Adaptive Variance Indicator (RAVI) were presented in the same article. Refer to the documentation on the VIDYA and RAVI studies for an explanation of their notation.

Let \(X\) be a random variable denoting the **Input Data**. Let the Inputs **Long VIDYA Length**, **Long Std Dev Length**, **Long Reference Standard Deviation**, **Short VIDYA Length**, **Short Std Dev Length**, **Short Reference Standard Deviation**, and **Turbo MACD Length** be denoted as \(n_V^{(L)}\), \(n_{\sigma}^{(L)}\), \(\sigma_{ref}^{(L)}\), \(n_V^{(S)}\), \(n_{\sigma}^{(S)}\), \(\sigma_{ref}^{(S)}\), and \(n_T\) respectively. Then we denote the **Turbo MACD** at Index \(t\) for the given Inputs as \(TMACD_t\left(X, n_V^{(L)}, n_{\sigma}^{(L)}, \sigma_{ref}^{(L)}, n_V^{(S)}, n_{\sigma}^{(S)}, \sigma_{ref}^{(S)}, n_T\right)\), and we compute it in terms of the RAVI as follows.

For \(0 \leq t < \max\left\{n_{\sigma}^{(L)}, n_{\sigma}^{(S)}\right\} - 2\):

\(\displaystyle{TMACD_t\left(X, n_V^{(L)}, n_{\sigma}^{(L)}, \sigma_{ref}^{(L)}, n_V^{(S)}, n_{\sigma}^{(S)}, \sigma_{ref}^{(S)}, n_T\right) = 0}\)For \(t > \max\left\{n_{\sigma}^{(L)}, n_{\sigma}^{(S)}\right\} - 2\):

\(\displaystyle{TMACD_t\left(X, n_V^{(L)}, n_{\sigma}^{(L)}, \sigma_{ref}^{(L)}, n_V^{(S)}, n_{\sigma}^{(S)}, \sigma_{ref}^{(S)}, n_T\right) = RAVI_t\left(X, n_V^{(L)}, n_{\sigma}^{(L)}, \sigma_{ref}^{(L)}, n_V^{(S)}, n_{\sigma}^{(S)}, \sigma_{ref}^{(S)}\right) - \left(\frac{2}{n_T + 1} \cdot RAVI_t\left(X, n_V^{(L)}, n_{\sigma}^{(L)}, \sigma_{ref}^{(L)}, n_V^{(S)}, n_{\sigma}^{(S)}, \sigma_{ref}^{(S)}\right) + \left(1 - \frac{2}{n_T + 1}\right) \cdot RAVI_{t - 1}\left(X, n_V^{(L)}, n_{\sigma}^{(L)}, \sigma_{ref}^{(L)}, n_V^{(S)}, n_{\sigma}^{(S)}, \sigma_{ref}^{(S)}\right)\right)}\)The big term after the subtraction sign is a sort of average of the RAVI. As noted in the documentation of the RAVI study, RAVI can be thought of as a sort of MACD. TMACD then can be thought of as the difference between the MACD and its average.

#### Inputs

- Input Data
- Long VIDYA Length
- Long Std Dev Length
**Long Reference Standard Deviation**: A scaling divisor. The volatility of the**Input Data**in the Long VIDYA is measured as a number of Long Reference Standard Deviations.- Short VIDYA Length
- Short Std Dev Length
**Short Reference Standard Deviation**: A scaling divisor. The volatility of the**Input Data**in the Short VIDYA is measured as a number of Reference Standard Deviations.- Turbo MACD Length

#### 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, 19th January, 2021.