Top 10 Essential Resources for Learning Financial Econometrics. Part #1 - Probability and Statistics Basics

Financial econometrics is an integral component of modern quantitative trading. Cutting edge systematic trading algorithms make extensive use of time-series analysis techniques for forecasting purposes. Thus, if you wish someday to become a skilled quantitative trader, it is necessary to have an extensive knowledge of econometrics.

The best way to start is to make sure that you are familiar with the essential basic probability and stastical concepts. 

If you have a weak background in probability and statistics, which would be the case if you didn't take these courses in college, then I would highly recommend reading the following Schaum's Outline book on the topic or digging out a copy of Probability and Random Processes by Grimmett and Stirzaker, which is a classic probability text. If however you've taken some solid probability courses while at college/university, then you may want to skip straight ahead to the Schaum's Outline on stats and econometrics (below). Thus the first set of recommended resources are:

Although I only personally have the 3rd edition of this book, I can confidently say that it is extremely useful in brushing up on your undergraduate probability and statistics.

The first part of the book begins with basic probability, random variables, probability distributions, expectation, correlation and ends with worked questions on special probability distributions. These distributions pop up everywhere within quant finance (normal, poisson, binomial, gamma, student's t etc), across derivatives pricing, risk management and quantitative trading.

The statistics section is significantly larger containing seven chapters across a wide range of beginner statistical concepts. Sampling and estimation theory are considered first, then hypothesis testing. Regression, ANOVA and finally Bayesian Methods are considered.

While the book is extremely comprehensive (it covers approximately two semesters of material), it does suffer from some typographical errors and is rather high level for a beginning course in statistics. It is a great supplement to a class or lecture series on the topic, however.

Yet another good book from the Schaum's Outlines stable. Salvatore and Reagle initially cover similar ground to Spiegal above, but spend far less time on pure probability.

The worked examples are excellent and the writing style is particularly engaging. After the first five chapters on statistics, estimation and hypothesis testing, the book gradually veers towards statistical methods as applied to econometrics. This includes simple and multiple regression, an essential tool in the econometricians toolbox.

A brief chapter on time-series methods is provided, discussing Autoregressive Moving Average (ARMA), stationarity and cointegration. These tools form the basis of some of the modern quantitative trading algorithms.

Note however that this book is not deep enough in econometrics to be read in isolation. It is really designed as a "bridge" between those who have taken an introductory probability/stats course and want to see slightly more challenging material. The main benefit, as with all Schaum's books, is that there are hundreds of worked examples. The book also includes a computational chapter on which the methods can be tested.