# Technical Studies Reference

### Clear Method Swing Line

This study displays Ron Black's Clear Method Swing Line for the Price Data. This study has no calculations; the study Subgraph is determined entirely by logical comparisons.

Let $$H_t$$ and $$L_t$$ be the values of the High Price and Low Price, respectively, at Index $$t$$.

We define five new quantities: the Highest High, the Highest Low, the Lowest High, the Lowest Low, and the Up Swing, and we denote their respective values at Index $$t$$ as $$HH_t$$, $$HL_t$$, $$LH_t$$, $$LL_t$$, and $$US_t$$, and these quantities are all initialized to zero. Note that, in the context of this study, "Highest" and "Lowest" do not refer to the simple maximum and minimum here. The determination of these quantities is more complicated than that, as we will explain below.

There are three cases to consider, and we will compute the above five quantities for each case. We will use superscripted case numbers to differentiate the cases. For instance, $$HH^{(1)}_t$$ is the Highest High for Case 1.

Case 1:

$$HH^{(1)}_t = \left\{ \begin{matrix} H_t & H_t > HH_{t - 1} \\ HH_{t - 1} & H_t \geq HH_{t - 1} \end{matrix}\right .$$

$$HL^{(1)}_t = \left\{ \begin{matrix} L_t & L_t > HL_{t - 1} \\ HL_{t - 1} & H_t \leq HL_{t - 1} \end{matrix}\right .$$

$$US^{(1)}_t = \left\{ \begin{matrix} 0 & H_t < HL^{(1)}_t \\ 1 & H_t \geq HL^{(1)}_t \end{matrix}\right .$$

$$LL^{(1)}_t = \left\{ \begin{matrix} L_t & H_t < HL^{(1)}_t \\ LL_{t - 1} & H_t \geq HL^{(1)}_t \end{matrix}\right .$$

$$LH^{(1)}_t = \left\{ \begin{matrix} H_t & H_t < HL^{(1)}_t \\ LH_{t - 1} & H_t \geq HL^{(1)}_t \end{matrix}\right .$$

Case 2:

$$LL^{(2)}_t = \left\{ \begin{matrix} L_t & L_t < LL^{(1)}_t \\ LL^{(1)}_t & L_t \geq LL^{(1)}_t \end{matrix}\right .$$

$$LH^{(2)}_t = \left\{ \begin{matrix} H_t & H_t < LH^{(1)}_t \\ LH^{(1)}_t & H_t \geq LH^{(1)}_t \end{matrix}\right .$$

$$US^{(2)}_t = \left\{ \begin{matrix} 1 & L_t > LH^{(2)}_t \\ 0 & L_t \leq LH^{(2)}_t \end{matrix}\right .$$

$$HH^{(2)}_t = \left\{ \begin{matrix} H_t & L_t > LH^{(2)}_t \\ HH^{(1)}_t & L_t \leq LH^{(2)}_t \end{matrix}\right .$$

$$HL^{(2)}_t = \left\{ \begin{matrix} L_t & L_t > LH^{(2)}_t \\ HL^{(1)}_t & L_t \leq LH^{(2)}_t \end{matrix}\right .$$

Case 3:

$$LL^{(3)}_t = \left\{ \begin{matrix} L_t & L_t < LL_{t - 1} \\ LL_{t - 1} & L_t \geq LL_{t - 1} \end{matrix}\right .$$

$$LH^{(3)}_t = \left\{ \begin{matrix} H_t & H_t < LH_{t - 1} \\ LH_{t - 1} & H_t \geq LH_{t - 1} \end{matrix}\right .$$

$$US^{(3)}_t = \left\{ \begin{matrix} 1 & L_t > LH^{(3)}_t \\ 0 & L_t \leq LH^{(3)}_t \end{matrix}\right .$$

$$HH^{(2)}_t = \left\{ \begin{matrix} H_t & L_t > LH^{(3)}_t \\ HH_{t - 1} & L_t \leq LH^{(3)}_t \end{matrix}\right .$$

$$HL^{(2)}_t = \left\{ \begin{matrix} L_t & L_t > LH^{(3)}_t \\ LH_{t - 1} & L_t \leq LH^{(3)}_t \end{matrix}\right .$$

Next, we consolidate the three cases as follows.

$$HH_t = \left\{ \begin{matrix} HH^{(1)}_t & US_{t - 1} = 1 \space and \space US^{(1)}_t = 1 \\ HH^{(2)}_t & US_{t - 1} = 1 \space and \space US^{(1)}_t = 0 \\ HH^{(3)}_t & US_{t - 1} = 0 \end{matrix}\right .$$

$$HL_t = \left\{ \begin{matrix} HL^{(1)}_t & US_{t - 1} = 1 \space and \space US^{(1)}_t = 1 \\ HL^{(2)}_t & US_{t - 1} = 1 \space and \space US^{(1)}_t = 0 \\ HL^{(3)}_t & US_{t - 1} = 0 \end{matrix}\right .$$

$$US_t = \left\{ \begin{matrix} US^{(1)}_t & US_{t - 1} = 1 \space and \space US^{(1)}_t = 1 \\ US^{(2)}_t & US_{t - 1} = 1 \space and \space US^{(1)}_t = 0 \\ US^{(3)}_t & US_{t - 1} = 0 \end{matrix}\right .$$

$$LL_t = \left\{ \begin{matrix} LL^{(1)}_t & US_{t - 1} = 1 \space and \space US^{(1)}_t = 1 \\ LL^{(2)}_t & US_{t - 1} = 1 \space and \space US^{(1)}_t = 0 \\ LL^{(3)}_t & US_{t - 1} = 0 \end{matrix}\right .$$

$$LH_t = \left\{ \begin{matrix} LH^{(1)}_t & US_{t - 1} = 1 \space and \space US^{(1)}_t = 1 \\ LH^{(2)}_t & US_{t - 1} = 1 \space and \space US^{(1)}_t = 0 \\ LH^{(3)}_t & US_{t - 1} = 0 \end{matrix}\right .$$

Finally, we denote the Clear Method Swing Line at Index $$t$$ as $$SL_t$$. This quantity is what appears in the study Subgraph, and we determine it as follows.

$$SL_t = \left\{ \begin{matrix} HL_t & US_t = 1 \\ LH_t & US_t = 0 \end{matrix}\right .$$

If $$US_t = 1$$, then the chart is in an Up Trend, and if $$US_t = 0$$, then the chart is in a Down Trend. The Subgraph is colored as follows.

• $$US_t = 1 \Rightarrow$$ Cyan
• $$US_t = 0 \Rightarrow$$ Magenta

#### Inputs

This study has no inputs.