## Center of Gravity by J. F. Ehlers

### Center of Gravity by J. F. Ehlers

Center of Gravity has a zero lag and allows to define turning points precisely. This indicator is the result of Ehler’s study of adaptive filters.

The indicator Center of Gravity allows identifying main pivot points almost without any lag. The idea of calculating a centre of gravity appeared from the investigation of lags of different filters with the finite impulse response (FIR) following the relative amplitude of filter coefficients. SMA (Simple Moving Average) is an FIR-filter, in which all coefficients have the same value. As a result, the centre of gravity of SMA is the exact centre of the filter. WMA (Weighted Moving Average) is an FIR filter, in which the last price change is weighted through the filter length, and so on.

The values of weighting are coefficients of filters. Coefficients of WMA filters can be presented as contours of a triangle. The centre of gravity is on 1/3 of the triangle base length. Thus WMA gravity centre is shifted to the right concerning the centre of gravitation of SMA of the same length, which gives us a smaller lag. For all examples, with FIR filters the sum of productions of coefficients and the price must be divided by the sum of coefficients for the preservation of original prices.

The most famous of such FIR filters is the Ehlers filter that can be presented the following way:

The Center of Gravity is calculated as Ehlers filter using the formula:

In this indicator the parameter Per=10 sets the period for the indicator calculation, the parameter PriceType=0 sets the price type, based on which the indicator is calculated – thus we get the main line (blue colour). For the signal line (red colour) the parameter SmoothPer=3 sets the period of smoothing the main indicator line, the parameter SmoothType=0 denotes the type of smoothing. The interpretation of the values of parameters is given in the form of comments in the indicator code.
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