Cyclic Polygamma Bands

The polygamma function is the (n+1)st derivative of the logarithm of the gamma function where n is the respective order. An approximation of this derivative at order n=1 is taken and applied to my own calculation of upper and lower bands (along with a mean), to create the cyclic polygamma bands. Cyclic, as it is weighted to mimic the local alternations in price (peak to trough corresponding to turning points of a set of moving averages). Lower cyclic weights for trending markets, higher cyclic weights correspond to choppier markets. It has 3 plots. The CP-H, CP-Mean and CP-L, where the CP-H is the red band, CP-L is the green band and CP-Mean the mean of these 2 bands. The method of trading is dependent on the user, but generally in an (here, undefined) uptrend, prices that snap the CP-L are considered bullish. Same logic for shorts and the CP-H.

The raw calculation is the unfiltered calculation. Cyclic is recommended, but the CP-Mean has exhibited interesting behavior (use at your own discretion). Cyclic aims to follow the local cycles of price.

Low cyclic weight will allow the weight of the polygamma to be higher. High cyclic weight will mimic price more, responding quicker to price. Use high if markets are chopping.

Versionsinformation:

Changed default cyclic weights to high. I've noticed low cyclic weights tends to be withdrawn from signaling considerably more, so the high option is set to default.