Reddit reviews Econometrics

Where are you in economics right now? Undergraduate? Graduate?

Advanced mathematics appears everywhere in economics, though your mileage may vary depending on your definition of "advanced". As a mathematician, I suspect that quantitative finance contains the most advanced mathematics, since in modern mathematics research the majority of interaction with economics is through quantitative finance. But unless you plan on doing the most advanced math, there's more than enough advanced math in non-finance economics to keep you interested.

Generally speaking, professional economists build up some skill in real and functional analysis, as well as a variety of other skills like optimization, stochastics, and PDEs, depending on their specific research interests. These are all graduate-level math topics, so I'd consider them reasonably advanced. Take a look into econ PhD prelim coursework. When I took the sequence, we used the texts Microeconomic Theory by Mas-Colell-Whinston-Green, Recursive Macroeconomic Theory by Ljungqvist and Sargent, and Econometrics by Hayashi. I think they're good springboards for you to evaluate the math in higher economics.

In quantitative finance, I'd maybe start by checking out Portfolio Risk Analysis by Connor, Goldberg, and Korajczyk, then if you're still interested, I'd pick up measure-theoretic probability. I recommend Probability with Martingales by Williams. Once you're comfortable with measure theory, look through Stochastic Calculus and Financial Applications by Steele. You'll very quickly enter the area of research mathematics while studying quantitative finance, e.g. jump-diffusion models and Levy processes appear in the pricing of exotic derivatives, and they're heavily studied by even pure mathematicians.

The important part of this question is what do you know? By saying you're looking to learn "a little more about econometrics," does that imply you've already taken an undergraduate economics course? I'll take this as a given if you've found /r/econometrics. So this is a bit of a look into what a first year PhD section of econometrics looks like.

My 1st year PhD track has used
-Casella & Berger for probability theory, understanding data generating processes, basic MLE, etc.

-Greene and Hayashi for Cross Sectional analysis.

-Enders and Hamilton for Time Series analysis.

These offer a more mathematical treatment of topics taught in say, Stock & Watson, or Woodridge's Introductory Econometrics. C&B will focus more on probability theory without bogging you down in measure theory, which will give you a working knowledge of probability theory required for 99% of applied problems. Hayashi or Greene will mostly cover what you see in an undergraduate class (especially Greene, which is a go to reference). Hayashi focuses a bit more on general method of moments, but I find its exposition better than Greene. And I honestly haven't looked at Enders or Hamilton yet, but they will cover forecasting, auto-regressive moving average problems, and how to solve them with econometrics.

It might also be useful to download and practice with either R, a statistical programming language, or Python with the numpy library. Python is a very general programming language that's easy to work with, and numpy turns it into a powerful mathematical and statistical work horse similar to Matlab.

Hey, so my favorite, whenever I want to go back and refresh myself on metrics is Fumio Hayashi. He writes it a bit like a novel and the flow is pretty good for the proofs. It can be a bit dense sometimes but I generally like his writing style. Also, he has you derive Nerlove's 1963 paper which is a good exercise in itself. Best of luck and go forth!

You should get a grad level econometrics text book or two to look for these. Here's one for instance,
http://www.amazon.com/Econometrics-Fumio-Hayashi/dp/0691010188

Why are you on this sub? You don't have any idea what you're talking about. Tell you what smart guy, go to your library and read Hayashi's seminal treatment of econometrics (Econometrics) and report back to us how it's political.