Finite Difference - Backward (mcbw_)

In calculus there exists a 'derivative', which simply just measures the difference between two points on a curve. For well behaved mathematical functions there are infinitely many points and so there exists a derivative at every point. Where there are infinitely many points in a curve that curve is called 'continuous'. Continuous curves are very nice to deal with since each point on it exists almost exactly where its neighbors are. However, if the curve does not have infinitely many points on it, but instead has a finite number of points on it, that curve is called 'discrete' instead of continuous. Taking the derivative of discrete curves is much trickier business since there are none of the mathematical conveniences that a continuous offers. In the real world everything we measure is a discrete curve, including Price (since we measure it a finite number of times, aka each candlestick)!

The branch of Discrete Mathematics has found an approach to measure the derivative along a discrete curve, that approach is aptly called "Finite Difference". To get a more accurate approximation of a discrete derivative, the finite difference approach uses weighted combinations of neighboring points. The most common type of finite difference is a 'central' difference, this uses a combination of points before and after the point of interest to approximate the discrete derivative. This is great for historical analysis but is not of much use for trading algorithms since it technically means using future prices to calculate the derivative of the current point. Instead we can use a less common variant called a 'Backwards Difference' that only uses a combination of points before the current one to help approximate the current derivative.

In this script you can choose the "Order" of your derivative and the "Accuracy" of its approximation. This script is for educational purposes for folks building trading algorithms. Many trading algorithms often have an element of seeing how much Price has changed from the previous candle to the current candle. This approach is the lowest accuracy derivative possible, and using the backwards finite differences, made available for the first time on TradingView (!!), algorithms that use derivatives can now have higher orders of accuracy!

Happy Trading/Developing!