Time Series (ST410016)
2010-2011

Aim

To make students familiar with the mathematical fundamentals of times series analysis.

Contents

(Strictly) stationary times series, projections and predictions, Central limit theorem for weakly dependent variables, nonparametric estimation of mean and covariances, spectral theory, ARMA and GARCH processes, state space models and the Kalman Filter, Yule-Walker, least squares and maximum likelihood estimation.

Prerequisites

Basic concepts of probability and measure theory, for instance at the level of Measure theoretic probability.

Literature

The course is based on A.W van der Vaart, Time Series. See also the comments and a list of errata.

Examination

Take home exercises and oral exam. Deadlines for homework: solutions have to be handed in within one week!

People

Lectures by Peter Spreij, homework grading by Naser Asghari.

Schedule

Spring semester, Thursdays 10:00 - 13:00, Location: Science Park 904, room D1.160; see the map of Science Park and the travel directions. The course will start on February 3. No classes on February 10, March 3, and not on March 24. No lectures on May 5, 19; Change of schedule: lecture 9 on April 21 (10:00-12:00), lecture 10 on April 21 (13:00-15:00 in D1.114), lecture 11 on April 28 (10:00-12:00), (last) lecture 12 on May 12 (10:00-12:00).

Examination

The final grade is a combination of the results of the take home assignments and the oral exam. To take the oral exam, you make an appointment for a date that suits your own agenda. If it happens that you'd like to postpone the appointment, just inform us that you want so. This is never a problem! The only important matter is that you take the exam, when you feel ready for it. Unavailable periods: May 19-25, June 2-8, 15-20, 24-29, July 25 - August 20. During the exam you will be asked about the theory only, you don't have to know all proofs by heart, but you should prepare for three theorems (your choice) a sketch proof, highlighting the main ideas.

Programme
(weekly updated, last modified: )

1
 Class: Chapter 1
Homework: Exercises 1.4, 1.9, 1.14, 1.29 (you don't have to be completely formal here, partial answers are also welcome)
2
 Class: Sections 2.1, 2.1, 2.3, 2.5, 2.6
Homework: Exercises 2.9, 2.12, 2.26, 2.28, 2.30
3
 Class: Sections 3.1 (briefly), 3.3, 4.1, 4.2
Homework: Exercises 4.2 (but for an MA process of order q), 4.3, prove the existence of the x_{n,l_n}->x just before Lemma 3.10; optional: 4.1 (probably hard) for a bonus.
4
 Class: Sections 4.3, (most of) 5.2
Homework: Read (briefly) Section 5.1, make Exercises 4.6, 4.9, 4.10, 5.2 (assume that the Z_t are IID)
5
 Class: Sections 3.6, 3.7, 5.3, 5.4, most of 6.1
Homework: Exercises 5.13, 6.4, 6.8, 6.18
6
 Class: Section 6.4 up to Theorem 6.32, Sections 8.1, 8.2 up to Theorem 8.8 (but not all details)
Homework: Exercises 6.23, 6.35, 8.7, 8.12
7
 Class: Section 8.2 from Definition 8.13, Section 8.3: Lemma 8.15 only, Sections 8.4, 8.6, 8.7
Homework: Read the introduction of Section 8.3, Example 8.16 and Section 8.5; make Exercises 8.19, 8.25, 8.31
8
 Class: Section 9.1 up to Theorem 9.9 and Theorem 9.15(i)
Homework: Read the remaining parts of Section 9.1, but you may skip the stuff on the Lyapunov exponent; make Exercises 9.5, 9.7, 9.10, 9.18
9
 Class: Sections 10.1, 10,2 10.3 (highlights)
Homework: Exercise 10.11 and the additional exercises
10
 Class: Sections 11.1, (11.2 hardly), 11.3
Homework: Exercises 11.2 (\alpha is an arbitrary vector), 11.21
11
 Class: Sections 12.1, 12.2, 12.3
Homework: Exercises 12.2, 12.6, 12.10, 12.11
12
 Class: Sections 13.1 - 13.4
Homework: Exercises 13.5, 13.6, 13.15, Extra Exercise 3 (and optional: Extra exercise 4)



Links

Korteweg-de Vries Institute for Mathematics
Master Stochastics and Financial Mathematics