# Technical Studies Reference

### Connie Brown Composite Index

This study calculates and displays the three indices that comprise Connie Brown's Composite Index.

Let $$X$$ be a random variable denoting the Input Data Input, and let $$n_{RSI}^{(1)}$$, $$n_{RSI}^{(2)}$$, $$n_M$$, $$n_{MA}^{(1)}$$, $$n_{MA}^{(2)}$$, and $$n_{MA}^{(3)}$$ denote, respectively, the RSI Length 1, RSI Length 2, Momentum Length, Moving Average Length 1, Moving Average Length 2, and Moving Average Length 3 Inputs.

We denote the three indices of the Connie Brown Composite Index for the given Inputs at Index $$t$$ as $$CBI^{(1)}_t\left(X,n_{RSI}^{(1)}, n_M, n_{RSI}^{(2)}, n_{MA}^{(1)}\right)$$, $$CBI^{(2)}_t\left(X,n_{RSI}^{(1)}, n_M, n_{RSI}^{(2)}, n_{MA}^{(1)}, n_{MA}^{(2)}\right)$$, and $$CBI^{(3)}_t\left(X,n_{RSI}^{(1)}, n_M, n_{RSI}^{(2)}, n_{MA}^{(1)}, n_{MA}^{(3)}\right)$$. These indices are all calculated for $$t \geq \max\left\{n_{RSI}^{(1)} + n_M, n_{RSI}^{(2)} + n_{MA}^{(1)} - 1\right\} + \max\left\{n_{MA}^{(2)} + n_{MA}^{(3)}\right\} - 1$$.

The first index is calculated in terms of the RSI, Momentum, and Simple Moving Average indicators as follows.

$$CBI^{(1)}_t\left(X,n_{RSI}^{(1)}, n_M, n_{RSI}^{(2)}, n_{MA}^{(1)}\right) = M_t\left(RSI\left(X,n_{RSI}^{(1)}\right), n_M\right) + SMA_t\left(RSI\left(X,n_{RSI}^{(2)}\right), n_{MA}^{(1)}\right)$$

Note: Depending on the setting of the Input Moving Average Type 1, the Simple Moving Average in the above formula could be replaced with an Exponential Moving Average, a Linear Regression Moving Average, a Weighted Moving Average, a Wilders Moving Average, a Simple Moving Average - Skip Zeros, or a Smoothed Moving Average.

Note: The Momentum calculation computed as type Difference, and not as type Quotient. That is, $$M_t\left(RSI\left(X,n_{RSI}^{(1)}\right), n_M\right) = RSI_t\left(X,n_{RSI}^{(1)}\right) - RSI_{t - n_M}\left(X,n_{RSI}^{(1)}\right)$$.

The second and third indices are Simple Moving Averages of the first one. They are calculated as follows.

$$CBI^{(2)}_t\left(X,n_{RSI}^{(1)}, n_M, n_{RSI}^{(2)}, n_{MA}^{(1)}, n_{MA}^{(2)}\right) = SMA_t\left(CBI^{(1)}\left(X,n_{RSI}^{(1)}, n_M, n_{RSI}^{(2)}, n_{MA}^{(1)}\right), n_{MA}^{(2)}\right)$$
$$CBI^{(3)}_t\left(X,n_{RSI}^{(1)}, n_M, n_{RSI}^{(2)}, n_{MA}^{(1)}, n_{MA}^{(3)}\right) = SMA_t\left(CBI^{(1)}\left(X,n_{RSI}^{(1)}, n_M, n_{RSI}^{(2)}, n_{MA}^{(1)}\right), n_{MA}^{(3)}\right)$$

Note: Depending on the setting of the Inputs Moving Average Types 2 and 3, the Simple Moving Averages in the above formulas could be replaced with Exponential Moving Averages, Linear Regression Moving Averages, Weighted Moving Averages, Wilders Moving Averages, Simple Moving Averages - Skip Zeros, or Smoothed Moving Averages.