SMA algorithm that accepts 'series' length

Indie’s standard indie.algorithms.Sma algorithm has a length parameter which cannot be dynamically changed. Its common usage looks like this: Sma.new(self.close, length=12), where the length parameter is typically a literal constant. While it is possible for the length to be a variable calculated at the time of indicator initialization or even during calculation over bars/candles, the general rule that should not be broken is as follows: once set, the value of the length parameter should not change. Otherwise, the algorithm breaks internally and starts giving inaccurate results*.

Sometimes, greater flexibility is needed. Fortunately, there is a way to achieve this, and this indicator with MySma algorithm demonstrates it. The algorithm is based on properties derived from prefix sums. Let’s look at an example to see how it works. Suppose we have a source series of values, src, like this:

src = …, 2, 7, 5, 4, 3, 9, 6

Think of this series as a series of close prices of some instrument on a chart. The last (i.e., current) value of this series is 6, which is accessed in Indie with the expression src[0].

To calculate the SMA with a length period, we simply divide the sum of length elements by the length value. The sum calculation seems straightforward, but it can be inefficient. For example, sum(src, length=3) is calculated as 3 + 9 + 6 = 18. This calculation is CPU-intensive, and the larger the length value, the more computationally expensive it becomes (the time complexity of this calculation is linear). This isn’t a big issue if the length is constant. However, consider a use case where length may vary from 2 to 300, and the size of the src series is around 20,000 bars, requiring SMA (and thus sum) calculations at every bar of this dataset. That would involve a lot of sum operations.

If we use prefix sums, which in Indie can be calculated with a cs = CumSum.new(src, length) statement, we can calculate sums in constant time (which is faster):

cs = …, 2, 9, 14, 18, 21, 30, 36

Calculation of any sum with any length using the cs series is as simple as subtracting two numbers. For example, sum(src, length=3) = cs[0] - cs[3] = 36 - 18 = 18. Let’s calculate sums with a few different lengths:

• sum(src, length=4) = cs[0] - cs[4] = 36 - 14 = 22, which is the same as 4 + 3 + 9 + 6 = 22
• sum(src, length=5) = cs[0] - cs[5] = 36 - 9 = 27, which is the same as 5 + 4 + 3 + 9 + 6 = 27

and so on. The general formula here is:

sum(src, length) = cs[0] - cs[length]

In this indicator, there are three SMA plot lines:

• The thin green and thin red lines both use the indie.algorithm.Sma from the standard library. They use different but constant length parameters: short_len and long_len. These two plots serve as references with which we compare the third plot.
• The thick light blue line uses the MySma algorithm described above, which is based on the prefix sums approach. MySma can accept a 'series' length, and depending on runtime conditions, either short_len or long_len is passed to it.

We see that the blue line is perfectly aligned with one of the two fixed-length SMA plots, proving its correctness.

This approach can be effectively used not only in the SMA algorithm but in any similar algorithm that can be calculated with the help of prefix sums or derivatives of SMA (like double-SMA and so on).

* This is true as of Indie v4.