Linear Models and Time-Series Analysis

1The Linear Model

The application of econometrics requires more than mastering a collection of tricks. It also requires insight, intuition, and common sense.

(Jan R. Magnus, 2017, p. 31)

The natural starting point for learning about statistical data analysis is with a sample of independent and identically distributed (hereafter i.i.d.) data, say , as was done in book III. The linear regression model relaxes both the identical and independent assumptions by (i) allowing the means of the to depend, in a linear way, on a set of other variables, (ii) allowing for the to have different variances, and (iii) allowing for correlation between the .

The linear regression model is not only of fundamental importance in a large variety of quantitative disciplines, but is also the basis of a large number of more complex models, such as those arising in panel data studies, time‐series analysis, and generalized linear models (GLIM), the latter briefly introduced in Section 1.6 . Numerous, more advanced data analysis techniques (often referred to now as algorithms) also have their roots in regression, ...