This is a self-contained and rigorous course in econometrics at the master and doctoral levels. This course is about fundamental knowledge in econometrics: asymptotics, unbiased and consistent estimations, constrained (restricted) estimations, and hypothesis testing.

This course does not only develop the theoies, but also provides serious disscussions on them. For example, we will discuss the interpretations of least squares (LS), maximum likelihood (ML), and generalized method of moments (GMM). We will discuss the meanings of consistency and identification. The theoretical details and the corresponding discussions are essential for applying econometrics.

The first part is asymptotics (large sample theory), which is about the probabilistic properties of random (stochastic) sequences when the sample sizes are very large (or diverge to infinity). We will start with the basic concepts of random processes and convergences, and then discuss two extremely important sets of theorems: laws of large numbers and central limit theorems.

The second part is unbiased and consistent estimation methods. The standard consistent methods in econometrics are LS, ML, GMM, and minimum distance. We will see that there is a unified theory of their consistency and asymptotic normality.

The third and fourth parts are respectively constrained estimations and hypothesis testing. These parts are based on the knowledge in the first two part.

We may discuss some interesting and important topics, such as shrinkage estimations, model selection, and Bayesian estimations.