TMS088 / MSA410 Financial time series Spring 21

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 online only!

The following program is preliminary and is regularly updated. Check the course home page often! A video lecture recorded last year is posted for each lecture and the content is discussed in online lectures. In addition, digital lecture notes are provided and possibly updated as the course progresses. You are advised to consult these rather than the slides below used in the recordings, which are only provided for completeness.


Lectures in form of discussion of the video content are on Tuesday, 10.00-11.45 and Thursday, 13.15-15.00, Zoom meeting ID 643 1858 2591, Password 445837. We recommend that you use these questions to guide you during your preparation through the content to help you to understand and formulate questions. The detailed schedule can be found in TimeEdit. Thanks to Leo for noise reduced versions of the videos to lecture 1 and 2.

Day Sections Video lectures Slides
23/3 Introduction to the course (Zoom recording from the first lecture) and introduction to time series (31:35)  Course info slidesSlides 1
25/3 [BD] 2.1

Stationary time series (01:03:38) 

Slides 2
13/4 [BD] 1.6, 2.4 Sample mean, sample autocovariance, hypothesis testing (46:40) Slides 3
15/4 [BD] 2.5 Forecasting stationary time series (01:32:00) *, Algorithms (49:14) Slides 4a, Slides 4b.
20/4 [BD] 1.5, 2.2, 6.4 Trend and seasonality (01:27:00), linear processes (26:41) Slides 5a, Slides 5b
22/4 [BD] 3.1-3.2 ARMA processes (01:01:36), (P)ACF for ARMA (31:18) Slides 6a, Slides 6b
27/4 [BD] 5.3-5.5 Parameter estimation for ARMA processes (01:16:29), Order identification/model building for ARMA processes (31:21) Slides 7a, Slides 7b
29/4 [BD] 3.3, 6.1-6.4 Forecasting of ARMA processes (30:42), SARIMA processes and unit root tests (42:39) Slides 8a, Slides 8b
4/5 [BD] 7.1-7.2, [T] 3 Introduction to (G)ARCH processes (01:06:25) Slides 9
6/5 [BD] 7.1-7.3, [T] 3 Parameter estimation and order selection for GARCH processes (01:04:46) Slides 10
11/5 [T] 3.6, 4.1 [BD] 7.3, 11.3 Extensions of GARCH models (49:19), Some nonlinear models (39:58) Slides 11a, Slides 11b
18/5 [T] 4.1, 4.2
[BD] 11.3
Testing for nonlinearities (52:27), Nonparametric methods (57:40) Slides 12a, Slides 12b
20/5 [T] 4.4 Forecasting and evaluation revisited (44:42) Slides 13
25/5 Interactive session with repetition and exam computation (Problem 1 - 2(b)) Material, see also the old course page
27/5 -

Continuation of the interactive session with exam computation (from Problem 2(c))

An exam example (01:44:45)

Slides 14, see also the old exam in the course pm

* At 32:25,  LaTeX: P(Z \neq 0) = 1 should be  LaTeX: P(Z\neq0)=0.

Recommended exercises

Day Exercises Video solutions
26/3 [BD] 1.1, 1.3*, 1.4, 1.6, 1.7 and  Extra exercises in basic probability (1, 3, 6 and 9 will be covered). Solutions
16/4 [BD] 2.1, 2.2, 2.3, 2.4, 2.7, 2.8, 2.14ab, 2.15, 2.20, 2.21


23/4 [BD] 1.10, 1.11, 1.12a, 1.13, 1.15, 3.1abcde, 3.3abcde, 3.6, 3.7, 3.8. Solutions
7/5 [BD] 3.4, 3.11, 5.3, 5.4abde, 5.8, 5.11, 5.12, 6.1. + Note on Project 1  Solutions
21/5 [BD]  1.8  and  additional ARCH and GARCH exercises (2, 4, and 6 will be covered). Solutions

[BD] 11.3 and Non-linear model exercises .


Detailed video solutions of the exercises in bold will be uploaded on the dates in the list above. You are expected to try to solve them on your own before the solutions are posted. 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 23 and May 26, 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  ShareLaTex, 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 and Mike will answer your questions there during lecture and 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