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# Technical Studies Reference

### 3/10 Oscillator

The 3/10 Oscillator is an MACD in which the Exponential Moving Averages are replaced with Simple Moving Averages. We will adopt the notation for the MACD here. The 3/10 Oscillator is so named because the default values of the Fast and Slow Moving Average Lengths are 3 and 10, respectively.

Let $$X$$ be a random variable denoting the Input Data Input. Let the Inputs Fast Moving Average Length, Slow Moving Average Length, and 3/10 Moving Average Length be denoted as $$n_F$$, $$n_S$$, and $$n_{3/10}$$, respectively. This study calculates and displays three indicators: the 3/10 Oscillator, the Moving Average of the 3/10 Oscillator, and the 3/10 Oscillator Difference. We denote the values of these indicators for the given Inputs at Index $$t$$ as $$MACD^{(3/10)}_t\left(X,n_F,n_S\right)$$, $$\overline{MACD^{(3/10)}}_t\left(X,n_F,n_S,n_{3/10}\right)$$, and $$\Delta MACD^{(3/10)}_t\left(X,n_F,n_S,n_{3/10}\right)$$, respectively. We describe the methods of calculation of these indicators below.

The 3/10 is calculated for $$t \geq \max\{n_F,n_S\}$$ as follows. Only the values for $$t \geq \max\{n_F,n_S\} + n_{3/10}$$ are displayed as output.

$$MACD^{(3/10)}_t\left(X,n_F,n_S\right) = SMA_t\left(X,n_F\right) - SMA_t\left(X,n_S\right)$$

The Moving Average of the 3/10 Oscillator is calculated for $$t \geq \max\{n_S,n_F\} + n_{3/10}$$ as follows.

$$\overline{MACD^{(3/10)}}_t\left(X,n_F,n_S,n_{3/10}\right) = SMA(MACD^{(3/10)}\left(X,n_F,n_S\right),n_{3/10})$$

In the above formula, $$MACD^{(3/10)}\left(X,n_F,n_S\right)$$ is a random variable denoting the 3/10 Oscillator with Inputs as listed in the parentheses.

The 3/10 Oscillator Difference is calculated for $$t \geq \max\{n_S,n_F\} + n_{3/10}$$ as follows.

$$\Delta MACD^{(3/10)}_t\left(X,n_F,n_S,n_{3/10}\right) = MACD^{(3/10)}_t\left(X,n_F,n_S\right) - \overline{MACD^{(3/10)}}_t\left(X,n_F,n_S,n_{3/10}\right)$$