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### Gann Swing Oscillator

This study calculates and displays the Gann Swing Oscillator (GSO) of the Price Data. The GSO is meant to be used in conjunction with the Gann HiLo Activator and the Gann Trend Oscillator, as prescribed by Robert Krausz in his article *The New Gann Swing Chartist*, Stocks & Commodities V16:2 (pp 57-66).

Let \(H_t\) and \(L_t\) be, respectively, the High Price and Low Price at Index \(t\).

Let \(H_t\) and \(L_t\) be, respectively, the High Price and Low Price at Index \(t\).

An Uptrend occurs at Index \(t\) if \(H_{t - 1} < H_t\) and \(L_{t - 1} < L_t\).

A Downtrend occurs at Index \(t\) if \(H_{t - 1} > H_t\) and \(L_{t - 1} > L_t\).

An Upswing occurs at Index \(t\) if \(H_{t - 1} > H_t\) and \(L_{t - 1} > L_t\) **and** \(H_t < H_{t + 1}\) and \(L_t < L_{t + 1}\). That is, an Upswing occurs at Index \(t\) if a Downtrend is immediately followed by an Uptrend at \(t\).

A Downswing occurs at Index \(t\) if \(H_{t - 1} < H_t\) and \(L_{t - 1} < L_t\) **and** \(H_t > H_{t + 1}\) and \(L_t > L_{t + 1}\). That is, a Downswing occurs at Index \(t\) if an Uptrend is immediately followed by a Downtrend at \(t\).

We denote the value of the **Gann Swing Oscillator** at Index \(t\) as \(GSO_t\), and we compute it for \(t > 1\) as follows.

Simply put, the value of GSO at Index \(t\) is 1 if an Upswing is immediately followed by two higher Highs, the value is -1 if a Downswing is immediately followed by two lower Lows, and if neither of these things occur then the previous value of the GSO is used.

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*Last modified Friday, 18th December, 2020.