# Technical Studies Reference

### Moving Average - Block

This study calculates and displays a block moving average for the Price Data.

Let $$H$$ and $$L$$ be random variables denoting the High and Low Prices, respectively, and let $$H_t$$ and $$L_t$$ be their respective values at Index $$t$$. Let the Average True Range Length, Box Multiplier 1, and Box Multiplier 2 Inputs be denoted as $$n$$, $$v_1$$, and $$v_2$$, respectively. We introduce two functions Work Box Half 1 and Work Box Half 2, denoted as $$WBH_t^{(1)}(n)$$ and $$WBH_t^{(2)}(n)$$, and we compute them in terms of the Average True Range as follows.

$$WBH_t^{(1)}(n) = \frac{1}{2}v_1\overline{TR}_t(n)$$

$$WBH_t^{(2)}(n) = \frac{1}{2}v_2\overline{TR}_t(n)$$

Next we introduce eight other functions which are calculated in terms of $$WBH_t^{(1)}(n)$$ and $$WBH_t^{(2)}(n)$$. They are Direction 1, Direction 2, Top 1, Top 2, Middle 1, Middle 2, Bottom 1, and Bottom 2, which we denote respectively as $$Dir^{(1)}_t(n,v_1)$$, $$Dir^{(2)}_t(n,v_2)$$, $$Top^{(1)}_t(n,v_1)$$, $$Top^{(2)}_t(n,v_2)$$, $$Mid^{(1)}_t(n,v_1)$$, $$Mid^{(2)}_t(n,v_2)$$, $$Bot^{(1)}_t(n,v_1)$$, and $$Bot^{(2)}_t(n,v_2)$$. These functions are all equal to zero for $$t < n - 1$$, and they are computed for $$t \geq n - 1$$ as follows $$(i = 1,2)$$

$$Dir^{(i)}_t(n,v_i) =\left\{ \begin{matrix} 1 & H_t > Top_{t - 1}^{(i)}(n,v_i) \\ -1 & L_t < Bot_{t - 1}^{(i)}(n,v_i) \space and \space H_t \leq Top_{t - 1}^{(i)}(n,v_i) \\ Dir^{(i)}_{n - 1}(n,v_i) & otherwise \end{matrix}\right .$$

$$Top^{(i)}_t(n,v_i) =\left\{ \begin{matrix} H_t & H_t > Top_{t - 1}^{(i)}(n,v_i) \\ Bot_t^{(i)}(n,v_i) + 2WBH_t^{(i)}(n) & L_t < Bot_{t - 1}^{(i)}(n,v_i) \space and \space H_t \leq Top_{t - 1}^{(i)}(n,v_i) \\ Top^{(i)}_{n - 1}(n,v_i) & otherwise \end{matrix}\right .$$

$$Mid^{(i)}_t(n,v_i) =\left\{ \begin{matrix} Top_t^{(i)}(n,v_i) - WBH_t^{(i)}(n) & H_t > Top_{t - 1}^{(i)}(n,v_i) \\ Bot_t^{(i)}(n,v_i) + WBH_t^{(i)}(n) & L_t < Bot_{t - 1}^{(i)}(n,v_i) \space and \space H_t \leq Top_{t - 1}^{(i)}(n,v_i) \\ Mid^{(i)}_{n - 1}(n,v_i) & otherwise \end{matrix}\right .$$

$$Bot^{(i)}_t(n,v_i) =\left\{ \begin{matrix} Top_t^{(i)}(n,v_i) - 2WBH_t^{(i)}(n) & H_t > Top_{t - 1}^{(i)}(n,v_i) \\ L_t & L_t < Bot_{t - 1}^{(i)}(n,v_i) \space and \space H_t \leq Top_{t - 1}^{(i)}(n,v_i) \\ Bot^{(i)}_{n - 1}(n,v_i) & otherwise \end{matrix}\right .$$

The Subgraphs that are displayed by Sierra Chart are the two Middle functions, $$Mid^{(i)}_t(n,v_i)$$ $$(i = 1,2)$$, and they are colored as follows.

• $$Dir^{(i)}_t(n,v_i) = 1 \Rightarrow$$ Cyan
• $$Dir^{(i)}_t(n,v_i) = -1 \Rightarrow$$ Magenta