Latest news
Welcome to the course! The schedule for the course can be found in TimeEdit.
The course representatives for the course are: Elias Kamyab Orvar (GU), Jacob Lindbäck (MPENM), Justin Lundgren (IE), James Pålsson (GU), Rami Sheik (IE), Aditya Sridhara (MPENM)
26/6: The exam is marked and everybody should have received the result in ladok. The exam tasks and solution are online now. Recall that you need 30 points (with bonus) to pass (GU: 30 for G, 45 for VG; Chalmers: 30 for 3, 40 for 4, 50 for 5). The reexam is scheduled for August 23 in the morning.
18/5: Fixed a couple of typos in the answer sheet.
15/5: If you missed the last lecture, do not forget to fill out the online evaluation. Everybody is welcome to the discussion of the results in the evaluation meeting on Monday 4/6, 13.00, in MVL22.
8/5: Bring a mobile device and the email that you receive before the next lecture to fill out the online evaluation during the last lecture on Tuesday 15/5.
27/4: We did not manage to cover the solution to Problem 5 on Project 1 in this week's exercise session, so we will do it next week instead.
24/4: There are many ways to define the BIC depending on the application. For Project 2, use (both for ARMA and GARCH models) the definition BIC = 2 logL + M*log(n), where logL is the loglikelihood of the model fit, M is the number of parameters estimated, and n is the sample size. This is the definition used by MATLAB in the function aicbic.
23/4: Project 2 is now online.
18/4: As stated in the lecture, please send your code for Project 1 both as mfiles and included in the pdf.
16/4: Typo fixed in Project 1. "Report both pvalues" in Task 2 should have been "Report all three pvalues".
13/4: The Project 1 text is now slightly updated. We made it more clear that after mean correcting all series, you may assume that they have zero mean and thus there is no need for a constant term (i.e. the a_0 in the notation of the lecture notes) when computing your predictions.
5/4: The problem is solved and exam registration for TMS088 is open and possible.
5/4: Although the exam registration opened yesterday, it seems not to be possible to register for the exam yet. Something in the administration went wrong such that the exam date is missing in the system. I will inform you as soon as I receive some feedback that it works. Please be patient! I am sorry for the inconvenience. Chalmers is working on the problem, so you do not have to contact the student center.
26/3: Proposition 2.3.5 in Project 1 refers to the numbering in the lecture/lecture notes.
26/3: We accept Swedish project reports but do not recommend it because you will need the Swedish vocabulary. We do not help you with that and do not accept Swenglish.
22/3: A student asked for templates for the project writing in the exercise class. You can find a lot of them on ShareLaTex. You can also find a couple of Swedish language templates at this link.
21/3: Project 1 is online.
Teachers
Course coordinator: Annika Lang
Teaching assistants: Andreas Petersson
Course literature
Main literature:
 [BD] P. J. Brockwell, R. A. Davis: Introduction to Time Series and Forecasting, 3rd edition, (free within Chalmers)
 [T] R. S. Tsay: Analysis of Financial Time Series, 3rd edition
Additional texts:
 [PS] M. A. Proschan, P. A. Shaw: Essentials of Probability Theory for Statisticians
 [LMN] E. Lindström, H. Madsen, J. N. Nielsen: Statistics for Finance
You might also be interested in:
 the slides from four years ago
 lecture notes written by J. Grandell at KTH
 [D] T. B. Driscoll: Learning MATLAB (free when accessed via the Chalmers library's catalogue)
Program
Lectures
Day 
Sections  Contents 

20/3 (1) 
Introduction to
the course, to time series and stationarity 

20/3 (2) 
[BD] 2.1, 2.4 
Characterization of stationarity 
23/3 
[BD] 1.6, 2.5 
Testing stationarity, forecasting stationary time series 
10/4 
[BD] 2.5 
forecasting stationary time series, DurbinLevinson 
12/4 
[BD] 2.5, 1.5  Innovations algorithm, trend and seasonality 
17/4  [BD] 1.5, 2.2, 3.1 
Trend and seasonality, linear processes, ARMA 
19/4  [BD] 3.1, 3.2, 5.1 
ARMA, ACVF, PACF, parameter estimation 
24/4  [BD] 5.2, 5.5, (3.3, 5.4), 7.2 [T] 3 
Parameter estimation with MLE, order selection, ARCH 
26/4  [BD] 7.2, 6 [T] 3 
GARCH, ARIMA 
3/5  [T] 4.1 
Task 5 of Project 1, nonlinear models, nonparametric methods for
model fitting 
8/5  [T] 4.1, 4.2 
Nonparametric methods for model fitting, Nonparametric nonlinearity tests 
15/5  [T] 4.2, 4.4 
Parametric nonlinearity tests, forecasting nonlinear models, evaluation, conclusion 
Recommended exercises
Day 
Exercises 

22/3  [BD] 1.1,
1.3*, 1.4, 1.6, 1.7 and exercises in basic
probability, at least 14. One or two of these extra
exercises will also be covered on the blackboard. 
13/4 
[BD] 2.1, 2.2,
2.3, 2.4, 2.7,
2.8, 2.14ab, 2.15**,
2.20, 2.21. Example
2.3.8 (from the lecture notes) will also be covered. 
20/4 
[BD] 1.11, 1.12a,
1.13, 1.15, 3.1abcde,
3.3abcde, 3.6, 3.7,
3.8. Some common questions about Project 1 will be
answered on the blackboard. 
27/4 
[BD] 3.4,
3.11, 5.3, 5.4abde***, 5.8,
5.11, 5.12. The solution to Project 1 will be covered along with
some notes on Project 2. 
4/5 
[BD] 1.8, 6.1 and additional
ARCH and GARCH exercises. From these we cover Exercise 12
on the blackboard. 
18/5 
2
nonlinear model exercises, solution to Project 2 and
repetition. Send an email to Andreas with blackboard topic
suggestions. 
Start with the black exercises and do the harder red ones when you have time.
Note that exercises marked in bold are discussed on the blackboard in the exercise session.
* Assume that the time series has a density (in terms of its finitedimensional distribution).
** Replace the condition "n > p" with "n >= p".
*** You may (and should) assume that the AR(2) model is causal.
See also the partial answer sheet from last year.
Computer labs
Reference literature:
Learning MATLAB, Tobin A. Driscoll ISBN: 9780898716832 (The book is published by SIAM).
Course requirements
The learning goals of the course can be found in the course plan.
Basic knowledge in probability theory and mathematical statistics. The assumed background is summarized in Chapter 1 of the lecture notes. Each student is responsible to make sure that he/she is familiar with this content.
Assignments
Two projects can be handed in for bonus points on the (first) ordinary
exam. You are encouraged to work in groups of two, and you are to write
one report per group. You may not work in groups of three or more.
Project 1: deadline 23/4.
Data: exchangerate.mat.
Project 2: deadline 7/5.
Data: sp500.mat.
Do not forget to read the project instructions carefully!
If you were enrolled in TMS087 earlier but did not pass the obligatory
moments, submit the projects before the deadlines to pass them. No bonus
points will be given.
General guidelines for report writing
The most important part of the bonus projects is writing a report that
reads well. It is vital for anyone working in a technical field to know
how to do this. You should write one complete report per group, and the
report should include wellcommented code. The report should preferably
be written in LaTex and not exceed 10 pages, including figures but
excluding code. For each figure and table you include in your report,
make sure to refer to it in your text and include a caption that
describes the content of the table/figure.
The report should be organised into subproblems, as the project itself.
For each problem, state the task you are going to solve using your own
words. Then describe how you solved the task. You should explain your
understanding of the problem and your theoretical strategy on how to
solve it when relevant. The implementation should also be described in
your own words. This can include, for example, mentioning what MATLAB
functions you used for solving the task. After this, state the result by
giving resulting numbers, plots etc. Comment on your results, interpret
and discuss if they are as you expected. Why or why not?
If you struggle with MATLAB, make sure to first of all consult the
documentation. For instance, if you want to find out how to calculate an
autocorrelation in MATLAB, google
it first. Make sure you read the documentation of every function
you use so you understand what it does. If you need further help, you
can access the book "Learning MATLAB" by T. B. Driscoll online for free
via the Chalmers Library. If you speak Swedish, you may also want to
consult the course pages for our own course Programmering
i MATLAB for lecture notes and other excellent resources.
If you have not used LaTeX before, the easiest way to get started is to
register for an account at ShareLaTex,
which is an online editor. Use your @student.chalmers.se email address
for registration in order to automatically get a premium account. For an
introduction to LaTeX, see Getting
Started with LaTeX for a guide in English or LaTeXtips
by Niklas Andersson and Malin Palö for a guide in Swedish.
Examination
A written exam (7.5 hp) has to be passed with at least 50% of the overall points which is graded with VG/G/U for GU students and 5, 4, 3, U for Chalmers students. Solutions and reports for home assignments should be sent as written on the problem sheet. Solutions or reports sent later than the deadlines will not be qualified for bonus points. For the exam you are allowed to bring four pages (two sheets) of your own handwritten notes and a simple calculator (which will not be necessary to solve the exam). You will be able to get up to 4 bonus points per project for good solutions which are valid at the (first) ordinary exam.
Examination procedures
In Chalmers Student Portal you can read about when exams are given and what rules apply on exams at Chalmers. In addition to that, there is a schedule when exams are given for courses at University of Gothenburg.
Before the exam, it is important that you sign up for the examination.
If you study at Chalmers, you will do this by the
Chalmers Student Portal, and if you study at University of
Gothenburg, you sign up via GU's
Student Portal.
At the exam, you should be able to show valid identification.
After the exam has been graded, you can see your results in Ladok by logging on to your Student portal.
At the annual (regular) examination:
When it is practical, a separate review is arranged. The date of the
review will be announced here on the course homepage. Anyone who can not
participate in the review may thereafter retrieve and review their exam
at the Mathematical
Sciences Student office. Check that you have the right grades and
score. Any complaints about the marking must be submitted in writing at
the office, where there is a form to fill out.
At reexamination:
Exams are reviewed and retrieved at the Mathematical
Sciences Student office. Check that you have the right grades and
score. Any complaints about the marking must be submitted in writing at
the office, where there is a form to fill out.
Old exams
Exam 2014/15 (first year with
a written exam) and its solution
Exam 2015/16 and its solution.
N.B.: In Problem 1, the
assumption that Cov(X_s,Z_t) = 0 for all time points s < t is
missing.
Exam 2016/17 and its solution
Exam 2017/18 and its
solution