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Technical Studies Reference


T3

This study calculates and displays a T3 Moving Average of the data specified by the Input Data Input. The study was developed by Tim Tillson.

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 the Input Length be denoted as \(n\), and let the Input Multiplier be denoted as \(v\). Then we denote the value of T3 at Index \(t\) for the given Inputs as \(T3_t(X,n,v)\), and we compute it using the following sequence of Exponential Moving Averages for the given Inputs.

\(EMA_t^{(1)}(X,n) = EMA_t(X,n)\)
\(EMA_t^{(2)}(X,n) = EMA_t(EMA(X,n),n)\)
\(EMA_t^{(3)}(X,n) = EMA_t(EMA(EMA(X,n),n),n)\)
\(EMA_t^{(4)}(X,n) = EMA_t(EMA(EMA(EMA(X,n),n),n),n)\)
\(EMA_t^{(5)}(X,n) = EMA_t(EMA(EMA(EMA(EMA(X,n),n),n),n),n)\)
\(EMA_t^{(6)}(X,n) = EMA_t(EMA(EMA(EMA(EMA(EMA(X,n),n),n),n),n),n)\)

In the above relations, \(EMA_t^{(j)}\) denotes the \(j-\)fold composition of the \(EMA\) function with itself, and \(EMA(X,n)\) is a random variable denoting the Exponential Moving Average of Length \(n\) for the Input Data \(X\). We compute \(T3_t(X,n,v)\) in terms of these Exponential Moving Averages for \(t > 0\) as follows.

\(T3_t(X,n,v) = -v^3EMA_t^{(6)}(X,n) + 3v^2(1+v)EMA_t^{(5)}(X,n) -v(1+v)^2EMA_t^{(4)}(X,n) + (1+v)^3EMA_t^{(3)}(X,n)\)

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.

T3.150.scss


*Last modified Wednesday, 03rd January, 2018.