Technical Studies Reference


Inverse Fisher Transform

This study calculates and both displays an Inverse Fisher Transform (IFT) and a Moving Average of the IFT for the data specified by the Input Data Input.

Let \(X\) be a random variable denoting the Input Data, and let \(X_t\) be the value of the Input Data at Index \(t\). Let \(n_{HL}\) denote the Highest Value/Lowest Value Length. We subject \(X_t\) to the following transformation.

\(\displaystyle{\xi_t(X,n_{HL}) = \frac{10\left(X_t - \min_t(X,n_{HL})\right)}{\max_t(X,n_{HL}) - \min_t(X,n_{HL})}} - 5\), \(\left(\max_t(X,n_{HL}) - \min_t(X,n_{HL}) \neq 0 \right) \)

In the above formula, \(\xi\) is the Greek letter "xi", \(\max\) is the Moving Maximum function, and \(\min\) is the Moving Minimum function.

Let the Input Data Mov Avg Length Input be denoted as \(n_I\). We denote the Weighted Moving Average of \(\xi_t(X,n_{HL})\) as \(\overline{\xi}_t(X,n_{HL},n_I)\), and we compute it as follows.

\(\overline{\xi}_t(X,n_{HL},n_I) = WMA_t(\xi(X,n_{HL}), n_I)\)

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

Let the Output Mov Avg Length Input be denoted as \(n_O\). We denote the Inverse Fisher Transform of \(\overline{\xi}_t(X,n_{HL},n_I)\) at Index \(t\) as \(IFT_t\left(\overline{\xi}(X,n_{HL},n_I)\right)\), and we compute it for \(t \geq n_I + n_O\) as follows.

For \(t = 0\):

\(IFT_0\left(\overline{\xi}(X,n_{HL},n_I)\right) = 0\)

For \(t > 0\):

\(\displaystyle{IFT_t\left(\overline{\xi}(X,n_{HL},n_I)\right) = \left\{ \begin{matrix} \frac{\exp\left(2\overline{\xi}_t(X,n_{HL},n_I)\right) - 1}{\exp\left(2\overline{\xi}_t(X,n_{HL},n_I)\right) + 1} & \max_t(X,n_{HL}) - \min_t(X,n_{HL}) \neq 0 \\ IFT_{t - 1}\left(\overline{\xi}(X,n_{HL},n_I)\right) & \max_t(X,n_{HL}) - \min_t(X,n_{HL}) = 0 \end{matrix}\right .}\)

We denote the Simple Moving Average of \(\overline{IFT}_t\left(\overline{\xi}(X,n_{HL},n_I)\right)\), and we compute it for \(t \geq n_I + n_O\) as follows.

\(\overline{IFT}_t\left(\overline{\xi}(X,n_{HL},n_I), n_O\right) = MA_t\left(IFT(\overline{\xi}(X,n_{HL},n_I)), n_O\right)\)

Note: Depending on the setting of the Input Output Mov Avg Type, 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.

Let the Line Value Input be denoted as \(l\). In addition to the graphs of \(IFT_t\left(\overline{\xi}(X,n_{HL},n_I)\right)\) and \(\overline{IFT}_t\left(\overline{\xi}(X,n_{HL},n_I)\right)\), this study displays horizontal lines at levels \(\pm l\).

Inputs

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.

Inverse_Fisher_Transform.226.scss


*Last modified Thursday, 26th July, 2018.