Moving Averages: Some Finer Properties by Giorgos E. Siligardos, PhD
Know Thy Weapons
What is the difference between the 10-period of a five-period moving average and a 15-period moving average? Does the sum of moving averages equal the moving average of the sum? How does the smoothing of a ratio differ from the ratio of smoothing? How can you algorithmically calculate the weights of a smoothing procedure? Find the answers to such technical questions here.
All technical analysts eventually engage in creating their own indicators and methods. And they all eventually use some kind of smoothing method to filter out noise. Various moving average methods can be used to smooth a series of values. In this article, I will discuss four interesting properties of simple and exponential moving averages (here-after referred to as SMAs and EMAs, respectively). These two averaging methods are the most popular in the technical analysis world, and their weighting scheme is simple, so they have clear and nice properties. Those who aspire to create indicators should find the concepts discussed here useful.