TMS088 / MSA410 Financial time series

Course PM

This page contains the program of the course: lectures, exercise sessions and projects. There are also guidelines on the discussion board. Other information, such as learning outcomes, teachers, literature, old exams and examination, are in a separate course PM. Please find the minutes from the mid-course meeting here.


All lectures and exercise sessions will be on campus only!

The following program is preliminary and is regularly updated. Check the course home page often!


Lectures will take place on campus on Tuesday, 10.00-11.45, in MVF31 and Thursday, 13.15-15.00, in Pascal. The detailed schedule can be found in TimeEdit

The lecture notes will be updated before each lecture containing the notes of the previous lectures and the upcoming one. Find below the link to the up to date version of the notes.

Day Sections Lecture notes Slides

Introduction to the course

Introduction to time series [LP] 2.1

Introduction to the course
24/3 [BD] 2.1 Stationary time series, autocorrelation function, statistical quantities [LP] 2.2-2.3
29/3 [BD] 1.6, 2.4, 2.5 Statistical quantities, tests for iid, introduction to forecasting, best preditors [LP] 2.3-2.4 Slides for Section 2.3
31/3 [BD] 2.5 Best linear predictors, Durbin-Levinson algorithm, lemma innovations algorithm [LP] 2.4 Slides used besides the blackboard
5/4 [BD] 2.5, 1.5, 6.4 Innovations algorithm, trend and seasonality [LP] 2.4-2.5 Slides additional to blackboard
7/4 [BD] 2.2, 3.1 Linear time series, ARMA models [LP] 3.1-3.2 Slides (besides blackboard)
26/4 [BD] 3.2, 5.3-5.5 ARMA models: (P)ACF, parameter estimation, order identification [LP] 3.2.1-3.2.4 Slides (besides blackboard)
28/4 [BD] 3.3, 6.1-6.4 ARMA models: forecasting, (S)ARIMA and unit root tests [LP] 3.2.5-3.3 Slides (besides blackboard)
3/5 [BD] 7.1-7.2, [T] 3 Introduction to GARCH models [LP] 4-4.1 Slides (besides blackboard)
5/5 [BD] 7.1-7.3 [T] 3 Parameter estimation, order selection and extension of GARCH models [LP] 4.2-4.4 Slides (besides blackboard)
10/5 [T] 4.1 [BD] 11.3 GARCH in practice, nonlinear models [LP] 5.1 Slides (besides blackboard)
12/5 [T] 4.1, 4.2
[BD] 11.3
Testing for nonlinearities, nonparametric methods [LP] 5.2-5.3 Slides (besides blackboard)
17/5 [T] 4.4 Bootstrapping, forecasting, and error measures [LP] 5.4 Slides (besides blackboard)
19/5 Theoretical task Project 1, old exam
24/5 Time series and SDEs, course evaluation, discussion of last quiz


Recommended exercises

The exercise sessions are on Friday 8:00-11:45 in MVH12. In the first two hours you have time to solve the exercises on your own or in groups. The teaching assistants will be there to help you.

At 10:00 the TKIEK-3 program can join an exercise session with Erik in MVF21. This exercise session will be in Swedish and in the first session during week 1, in addition to the exercises in the course literature, Erik will present some extra exercises adapting to the previous courses of the TKIEK-3 program. At the same time, Ioanna will present the exercises of the course literature in English in MVH12. Students of all programs are of course welcome to choose an exercise session. The exercise session with Erik is an additional help we offer to bachelor students, who feel that they may benefit from a session in Swedish with an extra opportunity to ask questions from the bachelor students' point of view. 


Day Exercises Additional Exercises

[BD] 1.1, 1.3*, 1.4, 1.6, 1.7 


Extra exercises in basic probability (136 and 9 will be covered)



For TKIEK: Erik kommer även att presentera några extra övningar i grundläggande sannolikhetsteori som en extra möjlighet till repetition. Länk till övningar .

1/4 [BD] 2.1, 2.2, 2.3, 2.4, 2.7, 2.8, 2.14ab, 2.15, 2.20, 2.21
8/4 [BD] 1.10, 1.11, 1.12a, 1.13, 1.15, 3.1abcde, 3.3abcde, 3.6, 3.7, 3.8.
22/4 drop in QA session for Project 1 see announcement, 10-12 in MVL15
29/4 [BD] 3.4, 3.11, 5.3, 5.4abde, 5.8, 5.11, 5.12, 6.1. 
6/5 [BD]  1.8  and  additional ARCH and GARCH exercises (2, 4, and 6 will be covered).

[BD] 11.3 and Non-linear model exercises .



QA session for Project 2

10-12 in MVH12

  You are expected to try to solve the exercises on your own before the solutions are presented in the exercise sessions. See also the partial answer sheet from three years ago.
* You may assume that the process has densities associated with its finite dimensional distributions.


2 computer projects in Matlab/R will be posted here during the course. They are not obligatory, but it's strongly recommended that you hand in a solution, and you can work in pairs. In total, you can get 8 bonus points (out of 60 in total) counting towards your exam score for good solutions. The deadlines are April 29 and May 27, respectively.

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 well-commented 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. You can also use Matalb's Live Editor (tutorial, video tutorial), or RStudio's RMarkdown (tutorial, video tutorial) to generate pdf reports containing your answers, code, and figures. A template using Matalb's Live Editor can be found here.

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  Overleaf, which is an online editor. Chalmers students can use their email address in the 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  LaTeX-tips  by Niklas Andersson and Malin Palö for a guide in Swedish.

Guidelines for the discussion board

There is discussion board available in the menu for you to put questions to regarding exercises and projects. You can write in equations directly, or you can photograph your calculations and upload them. Annika will answer your questions there during lecture, Erik and Ioanna will answer them during the exercise session hours. If time permits we will answer questions outside of this time as well. You are of course also welcome to send your questions to us via private messages in Canvas, but if possible try to put your questions to the discussion board. Then everyone can benefit from your help. You can respond to each other's questions in the board, too. This is very much encouraged, but try to only write hints and similar, since full solutions can discourage some to solve exercises on their own. We retain the right to delete such posts, and any other posts which violate the directions for the use of the IT resources at Chalmers.

Course summary:

Date Details Due