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Technical Studies Reference

Even Better Sinewave Indicator

This study calculates and displays an Even Better Sinewave Indicator (by John Ehlers) for the data given by the Input Data Input.

Let \(X\) be a random variable denoting the Input Data, and let \(X_t\) be the value of \(X\) at Index \(t\). Let the Length Input be denoted as \(n)\.

We begin by computing a constant that depends on the Length, which we denote as \(\alpha^{(1)}(n)\).

\(\displaystyle{\alpha^{(1)}(n) = \frac{1 - \sin\left(\frac{360^\circ}{n}\right)}{\cos\left(\frac{360^\circ}{n}\right)}}\)

If \(\cos\left(\frac{360^\circ}{n}\right) = 0\), then \(\alpha^{(1)}(n) = 0\).

We denote the High Pass Filter at Index \(t\) as \(HP_t(X,n)\), and we compute it as follows.

\(\displaystyle{HP_t(X,n) = \frac{1}{2}\left(1 + \alpha^{(1)}(n)\right)\left(X_t - X_{t - 1}\right) + \alpha^{(1)}(n) \cdot HP_{t - 1}(X,n)}\)

Note: The lowest possible setting for \(n\) is \(5\). This is because \(\alpha^{(1)} = 0\) for \(n = 2\), and \(\alpha^{(1)}\) is undefined for \(n = 4\). The lower limit of \(5\) is intended to prevent users from using either of these problematic settings.

Next, we compute a 2-bar Simple Moving Average of \(HP_t(X,n)\), as follows.

\(\overline{HP}_t(X,n) = SMA_t(HP(X,n),3)\)

We then denote the the Wave Amplitude and Wave Power as \(A_t(X,n)\) and \(P_t(X,n)\), respectively, and we compute them using a 2-Pole Super Smoother Filter on \(\overline{HP}_t(X,n)\), as follows.

\(A_t(X,n) = SSF^{(2)}_t\left(\overline{HP}(X,n),10\right)\)
\(P_t(X,n) = \left[A_t(X,n)\right]^2\)

We then compute the three-bar Simple Moving Averages of the Amplitude and Power, denoting these averages respectively as \(\overline{A}_t(X,n)\) and \(\overline{P}_t(X,n)\). We compute them as follows.

\(\overline{A}_t(X,n) = SMA_t(A(X,n),3)\)
\(\overline{P}_t(X,n) = SMA_t(P(X,n),3)\)

Finally, we denote the Even Better Sinewave Indicator as \(EBSWI_t(X,n)\), and we compute it as follows.

\(\displaystyle{EBSWI_t(X,n) = \frac{\overline{A}_t(X,n)}{\sqrt{\overline{P}_t(X,n)}}}\)

If \(\overline{P}_t(X,n) = 0\), then \(EBSWI_t(X,n) = 0\).


*Last modified Monday, 26th September, 2022.