Least Squares Methods, Theory.
Last week we shared on our Russian Doll Testing code.
This week we want to start off one of our initiatives on HangukQuant, which is to start developing core theoretical ideas in mathematics, statistical theory, computing and markets. Our newsletter will now span discussions across alpha strategies, coding as well as theory, and we will jump between these parallel and congruous subjects. In my opinion it is not possible to study one in isolation without developing appreciation across multiple core topics - quant trading is a practitioner’s science heavily built across many domains.
Eventually we look to develop these set of notes until it covers theory across linear algebra, statistics, calculus, stochastic calculus, algorithms, economics, information theory, alpha ideas, strategy performance, private notes, ruminations so on and so forth. The grand idea is to have a unifying and reflexive relationship between both theoretical and applied work that cross references seamlessly with each other. Of course this will almost certainly be a rather demanding task that has neither been achieved ever, but nevertheless our idea is that in the process of such a grand ultimate goal we arrive at an equally remarkable work that will be our tour de force.
Free readers will get snapshots of the notes that we write from time-to-time, and paid readers will get the full set of notes that will be continuously worked on and improved as we iterate through more material. These notes are written almost in real-time as part of my revision or even as part of my study of new quantitative methods - there are bound to be mistakes. It would be great if readers can correct the errata (spelling, math, intuition or otherwise). At points where I have yet to prove some sub-results or lemma I have put (verify this) as comment. At some point when the time permits I intend to come back and write the proofs at those junctures, however if readers want to offer their own proof in comments you are strongly encouraged to do so. I will include in footnote the credits of those meanigful corrections and sub-proofs I end up using. If you do send me a snapshot of those proofs in comments or in mail do include the name you wish to be addressed by.
Since the notes are written from referencing countless of sources such as books, forums, private notes, college notes, dicussions and so on, sometimes the terminology and notations might get mixed up. Usually each section/chapter is not self-contained, even though the final book is intended to be. We will cross-reference concepts by their numbering, which are digitally linked so that you can jump to the relevant sections when necessary. When it is not linked, it means that the theory was developed in part of the paper that I have not yet released to the public.
Here is a preview to our first post on Least Squares Methods, and is available for all readers to peruse:
