Discussing the article: "Category Theory in MQL5 (Part 22): A different look at Moving Averages"
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Check out the new article: Category Theory in MQL5 (Part 22): A different look at Moving Averages.
In this article we attempt to simplify our illustration of concepts covered in these series by dwelling on just one indicator, the most common and probably the easiest to understand. The moving average. In doing so we consider significance and possible applications of vertical natural transformations.
Category Theory’s application to Finance has been the mainstay of articles in these series. We have dwelt a lot on time series forecasting because it is pertinent to most traders and they are the majority of members on this platform. However other relevant applications outside of this do include valuation, risk, portfolio allocation and many others. And perhaps to do a quick rundown on a valuation example, there is a plethora of ways in which category theory could be applied in obtaining the valuation of a stock. For instance, if we take the key stock metrics to each be an object in a category, then the morphisms (or graph paths) linking across these different metrics (like revenues, debt, etc.) can be attributed to different valuation classes (say A+, A, B, etc.). With this, once we have a particular stock’s metrics, we can then quantify by how much it belongs to a particular class. This is a simplified approach that is only meant to serve as a hint to what could be done within this purview.
Sticking to time series though, moving averages though overlooked by some as being too simplistic, are very significant in technical analysis primarily because their concept is foundational to so many other indicators e.g. Bollinger Bands, MACD, etc. They could be thought of as a less volatile view of price action, and emphasis on the ‘less-volatile’ is important given the amount of white noise in the markets.
For this article we will continue with the theme on natural transformations we introduced in the last article by exploring the ability of natural transformations to bridge the gap between related data sets of different dimensions. ‘Dimensions’ here is used to represent column count within a data set. So as before we are faced with two categories, one of a ‘simple’ series of raw prices, and the other with a ‘compound’ series of moving average prices. Our purpose will be to show applications in time series forecasting with a scope of only three functors.
Author: Stephen Njuki