# Technical Studies Reference

### Ergodic

This study calculates and displays Bill Blau's Ergodic indicator, also known as the True Strength Index. This study calculates 3 lines, the Ergodic (True Strength Index), the Ergodic Signal Line (exponential moving average of the TSI), and the Ergodic Oscillator (Difference of Signal and TSI). Only the first is displayed, but the others can be displayed by going through Settings >> Subgraphs >> Draw Style and changing the setting to anything other than Ignore.

Let $$X$$ be a random variable denoting the Input Data, and let the Long MovAvg Length, Short MovAvg Length, Signal Line MovAvg Length, and Multiplier Inputs be denoted as $$n_L$$, $$n_S$$, $$n_{Sig}$$, and $$v$$, respectively. We denote the Ergodic, Ergodic Signal Line, and Ergodic Oscillator at Index $$t$$ for the given Inputs as $$TSI_t(X,n_L,n_S,v)$$, $$\overline{TSI}_t(n_L,n_S,n_{Sig},v)$$, and $$TSIOsc_t(X,n_L,n_S,n_{Sig},v)$$, respectively, and we calculate them in terms of Exponential Moving Averages as follows.

$$\displaystyle{TSI_t(X,n_L,n_S,v) = v\cdot\frac{EMA_t(EMA(\Delta X, n_L), n_S)}{EMA_t(EMA(|\Delta X|, n_L), n_S)}}$$

In the above formula, $$\Delta X_t = X_t - X_{t - 1}$$ is calculated for $$t \geq 1$$, the first EMA is calculated for $$t \geq n_L - 1$$, and the second EMA is calculated for $$t \geq n_L + n_S - 2$$.

$$\overline{TSI}_t(X,n_L,n_S,n_{Sig},v) = EMA_t(TSI(X,n_L,n_S,v), n_{Sig})$$

$$TSIOsc_t(X,n_L,n_S,n_{Sig},v) = TSI_t(X,n_L,n_S,v) - \overline{TSI}_t(X,n_L,n_S,n_{Sig},v)$$

Each of the above is calculated for $$t \geq n_L + n_S + n_{Sig} - 3$$.

Note: Depending on the setting of the Input MovAvg Type, the Exponential Moving Averages in the above formulas could be replaced with Linear Regression Moving Averages, Simple Moving Averages, Weighted Moving Averages, Wilders Moving Averages, Simple Moving Averages - Skip Zeros, or Smoothed Moving Averages.

#### Inputs

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.