# Technical Studies Reference

### Tenkan-Sen

This study calculates and displays the Tenkan-Sen study for the data specified by the Input Data High and Input Data Low Inputs.

Let $$X^{(High)}$$ and $$X^{(Low)}$$ be random variables denotining Input Data High and Input Data Low, respectively, and let $$X_t^{(High)}$$ and $$X_t^{(Low)}$$ be their respective values at Index $$t$$. Let the Tenkan-Sen Length be denoted as $$n_{TS}$$.

We denote the maximum value of $$X_t^{(High)}$$ and the minimum value of $$X_t^{(Low)}$$ over a moving window of $$n_{TS}$$ chart bars terminating at Index $$t$$ as $$\max_t(X^{(High)},n_{TS})$$ and $$\min_t(X^{(Low)},n_{TS})$$, respectively. These are computed for $$t \geq n_{TS} - 1$$ as follows.

$$\max_t\left(X^{(High)},n_{TS}\right) = \max\left\{X_{t - n_{TS} + 1}^{(High)},...,X_t^{(High)}\right\}$$

$$\min_t\left(X^{(Low)},n_{TS}\right) = \min\left\{X_{t - n_{TS} + 1}^{(Low)},...,X_t^{(Low)}\right\}$$

We denote the value of Tenkan-Sen at Index $$t$$ for the given Inputs as $$TS_t\left(X^{(High)}, X^{(Low)}, n_{TS}\right)$$, and we compute it for $$t \geq n_{TS} - 1$$ as follows.

$$TS_t\left(X^{(High)}, X^{(Low)}, n_{TS}\right) = \displaystyle{\frac{\max_t\left(X^{(High)},n_{TS}\right) + \min_t\left(X^{(Low)},n_{TS}\right)}{2}}$$

This study is mathematically identical to the Kijun-Sen study. The only difference between the two is that Tenkan-Sen has a default length of $$n_{TS} = 9$$, while Kijun-Sen has a default length of $$n_{KS} = 26$$.