# Technical Studies Reference

### 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.