EhlersCenterOfGravity

Summary

EhlersCenterOfGravity is RTTA's streaming center-of-gravity (CG) oscillator from John Ehlers. Over a rolling price window it measures the "balance point" of the price path and recenters it so the oscillator fluctuates about zero. The prior CG is returned as lag for trigger-style crosses.

Update API

result = rtta.EhlersCenterOfGravity(window=10, fillna=True).update(price)

Parameter	Default	Meaning
`window`	`10`	Rolling lookback (minimum 2)
`fillna`	`True`	If `False`, NaN until the window is full

update(...) returns:

cg — current center-of-gravity oscillator
lag — previous bar's cg (for cross signals)

advance(price) updates state; last() returns the cached result.

Theory Of Operation

Treat the last \(n\) prices as point masses of equal mass along a bar axis. Ehlers assigns weight \(1\) to the newest bar and weight \(n\) to the oldest, so the first moment is biased toward older prices when the market has been falling into the window and toward newer prices when it has been rising. Dividing by the sum of prices (not sum of weights) yields a raw CG coordinate; subtracting \((n+1)/2\) centers the null at the geometric mid-window so the oscillator is roughly zero-mean.

Because CG leads ordinary smoothed oscillators at turning points, Ehlers often plots CG against its one-bar lag; RTTA exposes that lag as the lag field.

Recurrence

Let \(n\) be the current number of buffered prices (\(n \le W\), \(W\) the constructor window). Index \(i=0\) as the newest sample and \(i=n-1\) as the oldest. Weights \(w_i = i+1\) (newest weight 1, oldest weight \(n\)):

\[N_t = \sum_{i=0}^{n-1} w_i\, x_{t-i},\qquad D_t = \sum_{i=0}^{n-1} x_{t-i}\]

\[CG_t = \begin{cases} 0 & \text{if } D_t = 0 \\ -\dfrac{N_t}{D_t} + \dfrac{n+1}{2} & \text{otherwise} \end{cases}\]

\[lag_t = CG_{t-1}\]

(with \(lag\) for the first bar equal to the constructor seed 0.0 before any update).

When fillna=False and the rolling buffer is not yet full, both fields are NaN. When fillna=True, partial windows use the available \(n\) samples with the same weight convention.

Implementation Notes

Implemented in src/rtta/indicator.cpp in class EhlersCenterOfGravity.
Result type: EhlersCenterOfGravityResult (cg, lag).
Uses RollingBuffer prices_; newest is prices_.at(n-1), matching the loop prices_.at(n - 1 - i) for weight index \(i\).
Batch helper: batch_ehlers_cg.

Summary

Update API

Theory Of Operation

Recurrence

Implementation Notes

Reference