This course is devoted to the problem of conducting asymptotically valid inference in autoregressive models. More specifically, we shall develop the machinery needed to construct confidence sets for:
the autoregressive coefficient in a first-order autoregressive model; and
the sum of the autoregressive coefficients (a measure of persistence) in a higher-order autoregressive model;
although almost all of our time will be devoted to the first of these. The ground that we shall cover includes the familiar territory of "unit root testing", but a successful resolution to the problem of confidence set construction will require us to go far beyond that. As we shall see, the autoregressive model provides a prototypical example of a "non-standard inferential problem", variants of which also arise in other areas of econometrics (such as in weakly and partially identified models) -- and so this course will also, albeit indirectly, provide you with an introduction to the methods used to conduct valid inference in such settings.
Similarly to last term's course, the emphasis in this course will be on the arguments needed to rigorously justify the inferential procedures under study (e.g. proving that tests and confidence sets have the claimed asymptotic size, etc.). The surest way to become familiar with these arguments is to work carefully through the proofs and -- most importantly -- attempt the exercises that I provide (in the course notes). You can only be sure that you really understand this material if you are able to complete (at least some of) the exercises.
Lectures will be held on Tuesday and Friday of Weeks 7-8. Tuesday lectures are at 11:30--13:00, and Friday lectures at 9:30--11:00, all in Seminar Room C (Manor Rd).
The only required readings are the course notes (below). Relevant background material is provided by Sections 3-5 and 10 of the notes from Bent's macroeconometrics course (Oxford IP required). I shall also draw freely upon certain fundamental results connected with convergence in probability and convergence in distribution, as were covered in Section 2 of the notes from my course on extremum estimators. You might therefore find it helpful to quickly review the indicated sections of both these sets of notes.
For those of you who would also like a somewhat less technical treatment of the ideas discussed in this course, you could consult either of the following graduate-level textbooks:
Hayashi (2000), Advanced Econometrics, Chapters 6 & 9.
Hamilton (1994), Time Series Analysis, Chapters 1-5 & 15-17.
These books should also provide you with some broader context for the material covered in this course, which -- largely for reasons of time -- will be almost entirely limited to first-order autoregressive models.
The course notes will also provide references to a range of relevant papers and monographs.
These will be posted during the course; my aim is to make the relevant sections available before we cover them in class. I will start posting solutions to the exercises from week 8 onwards. A clear indication of how I expect you to prepare for the exam will be provided in due course: but for the time being, you should focus your revision on the material covered in Section 3 of the notes. Please note that you can skip the material in any of the starred sections without loss of continuity; nor is that material examinable.
Univariate autoregressions: an introduction [updated 07/03]
'Stationary' asymptotics [updated 24/05]
'Unit root' asymptotics [updated 12/04: Section 3.6.2 significantly changed (on 11/04)]
Uniform distributional approximation [not examinable]
Errata [updated 24/05]
Solutions to exercises [24/05: solutions to all exercises from Sections 2 and 3]
Specimen exam question
Since this is the first time that I have taught from these notes, they will undoubtedly contain some errors: please email me if you find any.