# TMA4285 - Time Series

TMA4285 - Time Series

To prevent the spread of COVID-19 infection on NTNU’s campuses, we ask you to follow the advice on this page. After each lecture you should fill out a form for R3 or
H1 due to the need for quick follow-up from the infection control office in case an infected person has been present in the room.
Remember 1 meter.

**Messages:**

09.12.2020: 2 fail, 1 blank, 19 pass. November 2020 LF Gandalf solution → UPPDATE

12.11.2020: A more current problem is time series for Covid19. You have done a good job here! It seems to be concluded by most groups that the noise is better modelled by a GARCH. This is a novel finding for these data.

11.11.2020: Example of current research on correlation.

04.11.2020: Due to Covid 19 the exam will be a home exam with pass/fail grading. More information below.

21.09.2019: This week we start on the statistics part of the course, and will talk about:

04.09.20: The first mandatory project is posted. See further down.

02.09.20: Solutions to exercises are posted approximately two weeks after they have been announced. For example, the solution to the first set of exercises will be posted on Friday 04.09.20.

16.08.20: To prevent the spread of COVID-19 infection on NTNU’s campuses, we ask you to follow the advice on this page. After each lecture you should fill out a form for R3 or H1 due to the need for quick follow-up from the infection control office in case an infected person has been present in the room.

06.07.20: Welcome to the course! The first lecture will take place in R3 Wednesday August 19. The lectures will be given in English if any non-Scandinavian speaking students attend the lectures.

**Teaching Material:**

Brockwell and Davis: Introduction to Time Series and Forecasting, Springer
2016 (3.Ed)

**Supplemental Reading:**

For some concepts and proofs if you happen to skip some lectures:

Brockwell and Davis: Time Series: Theory and Methods, Springer
1991 (2.edition)

For R examples needed for mandatory excercises:

Shumway and Stoffer: Time Series Analysis and Its Applications (With R Examples),
Springer 2017.

Venables, Ripley (2002). Modern applied statistics with S (4th ed.).
New York: Springer. Chapter 14: Time Series Analysis

Miscellany:

GUM (2008): Bureau International des Poids et Mesures, Guide to the Expression of Uncertainty in Measurement

The ISI glossary of statistical terms in a number of languages

Box, Jenkins, Reinsel (2008): Time Series Analysis (Forecasting and Control) (4th ed.), Wiley

** Recommended preliminary courses:**

TMA4267 - Linear Statistical Models (Multivariate regression)

TMA4265 - Stochastic Modeling (Stochastic processes)

TMA4145 - Linear Methods (Vector- and Hilbert space)

** A more advanced related course:**

MA8109 - Stochastic Processes and Differential Equations

**Teachers:**
Gunnar Taraldsen and
Jorge Parada

**Reference group:**

Eivind Hagemann Brataas (MAT), Jens Berg-Jensen (MLREAL), Marion Helen Røed (Vikar: Stephanie ) (INDMAT)

02.10.19: Meeting 1

06.11.19: Meeting 2

18.12.19: Meeting 3

**Lectures:**

Wednesday 12:15-14:00 R3 Realfagsbygget

Friday 08:15-10:00 H1 Hovedbygget

**Exercises:**

Tuesday 16:15-17:00 H1 Hovedbygget

**Consultance time:**

Wednesday 14:15-15:00 Room 1138, Sentralbygg 2, Gløshaugen

**Lecture Plan: Brockwell and Davis 2016 **

Week 34: Stochastic processes and Hilbert space of random variables, Chap 1 and 2. App A, B, C

Week 35: Stationary processes and prediction, Chap 2. List of notation

Week 36: Stationary processes, Chap 2. The Wold Decomposition

Week 37: No lectures. **Work on Exercise 3**

Week 38: ARMA models, Chap 3

Week 39: Statistics for ARMA models, Chap 5

Week 40: Statistics for ARMA models, Chap 5

Week 41: Nonstationary and seasonal time series, Chap 6.1-5

Week 42: Time Series Models for Financial Data, Chap 7.1 Historical Overview, 7.2 GARCH Models

Week 43: No lectures. **Work on Excercise 8**

Week 44: Chap 9 State-Space Models, Chap 9.1-5

Week 45: December 2018
LF Repetition

Week 46: December 2009
LF Repetition

Week 47: November 2019
LF Repetition

Main ideas in the course. Repetition. Exam questions.

**Exercises:** (Preliminary plan updated as we go!) from
BD and
GT

Ex 1, Week 35: **GT**: 1, **BD**: App A: 4,5,6, Chap 1: 2-5,8 Chap 2: 1.
LF

Ex 2, Week 36: **GT**: 2, **BD**: Chap 2: 5, 7-9, 13, 15, 18-20. LF

Ex 3, Week 37: Mandatory! The deadline for submission is Sunday September 20th (23:59). Send the report by email to Jorge. Remember to include the names of all group members. Exercise 3,
CSV,
XLS,

Ex 4, Week 39: **GT**: 3, **BD**: Chap 3: 1b, 4, 6, 7, 8, 12.
LF

Ex 5, Week 40: **GT**: 4, **BD**: App A: 7, Chap 5: 1,3,4,8,13.
LF

Ex 6, Week 41: **GT**: 5, **BD**: Chap 5: 9, 10, 11, 12.
LF

Ex 7, Week 42: **GT**: 6, **BD**: Chap 6:1, 2, 5, 6, 11.
LF

Ex 8, Week 43: Mandatory!
The deadline for submission is Sunday November 1th (23:59). Send the report by email to Jorge. Remember to include the names of all group members. Exercise 8,
CSV,
XLS,

Ex 9, Week 45: Chap 7: 1, 2, 3.
LF

Ex 10, Week 46: Chap 9: 1, 3, 9, 11, 12, 17.
LF

Week 47: Previous exams and exercises

**Exam (80/100):**
Handwritten home exam with Pass/Fail grading, 25.11.2019, 4 hours.
Collaboration is not allowed and is considered as cheating with corresponding possible consequences.
Both the exam and the two mandatory exercises must result in Pass to obtain Pass in the course.

Eksamen skal gjennomføres på samme dato og innenfor samme tidsramme som opprinnelig oppsatt. Det vil bli en digital eksamen i Inspera. Alle hjelpemidler er tillatt. Bestått/ikke bestått benyttes i emnet.

Oppgaven har samme form som ved ordinær skriftlig eksamen. Besvarelser SKAL skrives for hånd og scannes via mobiltelefon over til PDF som lastes opp til Inspera. Det er en fordel om du har forsøkt å fotografere et større dokument og lagre som pdf på egen PC før eksamen. Oppskrift på lagring til PDF.

Mer informasjon om digital vurdering . Demoeksamen viser fasongen til prøven, men opplasting av besvarelse kan ikke prøves med den. Innlogging på Inspera gir adgang til flere andre demoeksamener hvor det også er mulig å laste opp besvarelse for uttesting på forhånd.

**Work (20/100):**
Two exercises are mandatory and should be handed in to Jorge.

**Curriculum: (preliminary plan) **

1) Exercises

2) Lectures (in particular definition and use of conditional expectation and Hilbert space theory - which is not in the book)

3) Chapters from Brockwell and Davis 2016:

1. Introduction
2. Stationary processes
3. ARMA models
4. Spectral analysis (out)
5. Modeling and forecasting with ARMA processes
6. Nonstationary and seasonal time series models (6.1-5)
7. Time Series Models for Financial Data (7.1-2)
8. Multivariate time series (out)
9. State space models (9.1-9.5)
10. Forecasting techniques (out)
Appendix A, B, C