[eachro]

I'd love to see linear regression taught by say a quant researcher from Citadel. How do these guys use it? What do they particularly care about? Any theoretical results that meaningfully change the way they view problems? And so on.

[mikaeluman]

I have some experience. Variants of regularization are a must. There are just too few samples and too much noise per sample.

In a related problem, covariance matrix estimation, variants of shrinkage is popular. The most straight forward one being Linear Shrinkage (Ledoit, Wolf).

Excepting neural nets, I think most people doing regression simply use linear regression with above type touches based on the domain.

Particularly in finance you fool yourself too much with more complex models.

[fasttriggerfish]

Yes these are good points and probably the most important ones as far as the maths is concerned, though I would say regularisations methods are really standard things one learns in any ML / stat course. Ledoit, Wolf shrinkage is indeed more exotic and very useful.

[Ntrails]

> There are just too few samples and too much noise per sample.

Call it 2000 liquid products on the US exchanges. Many years of data. Even if you approximate it down from per tick to 1 minutely, that doesn't feel like you're struggling for a large in sample period?

[kqr]

It sounds like you are assuming the joint distribution of returns in the future is equal to that of the past, and assuming away potential time dependence.

These may be valid assumptions, but even if they are, "sample size" is always relative to between-sample unit variance, and that variance can be quite large for financial data. In some cases even infinite!

Regarding relativity of sample size, see e.g. this upcoming article: https://two-wrongs.com/sample-unit-engineering

[bormaj]

They may have been referring to (for example) reported financial results or news events which are more infrequent/rare but may have outsized impact on market prices.

[energy123]

If the distribution changes enough, multiple years of data may as well be no data.

[ljosifov]

The linear regression - and with a single predictor at that - is the workhorse. As if - the cross-product x'*y is too little, divided by dot-product x'*x is just right (regression), and dividing it again by another dot-product y'*y (correlation, with the sqrt) would be over-doing it. :-)

There is no big mystery I'm afraid, there is no big reveal. It's as Jim Simons described in the Numberphile video interview: a slow painstaking accumulation of weak signals, plus crafting and improving various boxes of the system. (the interfaces between them are largely known) The fitting method used does not buy that much in the grand scheme of things - as long as it does not ruin things, that is.

(I've not been at Citadel but been quant R&D&trading last 20yrs)