# Technical Studies Reference

- Technical Studies Reference
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- Using Studies (Opens a new page)

# 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.

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 \(n_{KS} = 26\).

#### Spreadsheet

The spreadsheet below contains the formulas for this study in Spreadsheet format. Save this Spreadsheet to the Data Files Folder.

Open it through **File >> Open Spreadsheet**.

*Last modified Monday, 03rd October, 2022.