This course is devoted to the problem of conducting asymptotically valid inference in autoregressive models. For reasons of time, we shall concentrate almost entirely on the first-order autoregressive model. 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 somewhat beyond that.
Similarly to last term's course, the emphasis in this course will be on the arguments needed to rigorously derive the asymptotic properties of the inferential procedures under study. 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 5-6. Tuesday lectures are at 11:30--13:00, and Friday lectures at 9:30--11:00, all in Seminar Room A (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 briefly 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.
An almost complete set of notes (missing Section 4), including solutions to most exercises; posted 12/02
We shall devote most of our time to the material in Section 3: so in terms of preparing for the exam, it is essential that you have a sound grasp of the material from that section.
Please email me if you find any errors in the notes.
In an exam, you can expect to be given copies of the following results, if any of these are relevant to answering the question: Lemmas 2.1, 2.2, 3.3, 3.4, 3.5, 3.6, 3.7.
As an aid to revision, I would particularly recommend working through the exercises in Section 3.6 of the notes.
If you are asked a question whose solution involves rewriting a (standardised) sum as a function of a stochastic process, as per (3.17) in the notes, I do not expect you to reproduce the detailed justification given in the notes; you may assert the equality without justification. The same holds for such an equality as (3.26), i.e. you may simply assert the appropriate stochastic integral representation.
'Specimen' exam question from last year (note this is probably too long for an exam question). [Solutions to be posted.]