# TMA4285 Time Series Models, Autumn 2016

## Messages

Dec. 21: The grades should be available on studweb shortly. Most of you did quite well, the model identification problem was perhaps not entirely unambiguous so this point has been graded leniently. For example, you don't loose any points for choosing a period of 11 for the seasonal model based on the peak at 11 in the pacf (this is indeed possible even though the true period is 12 apparent from the more easily interpretable acf). If anyone wants "begrunnelse" you can send me an email (note that I can not give you the exact score). Happy holidays to everybody!

Dec. 9: A preliminary solution to the exam is available below.

Dec. 7: I'll be available at the exam around 10:30 tomorrow so if you have any questions you should have them prepared by then.

Dec. 7: Now you can pick up your project reports in Xin's office (1026).

Dec. 4: An error in eq. (4) in the Lecture summary has been corrected (the inner sum goes from j=0 and not j=1).

Dec. 2: On December 6, from about 12:15-16 (two days before the exam) I'll be available to answer questions at R4 (EU1 in Realfagsbygget). If I'm not there send me an email or text message to 99705519.

Dec. 1: Permitted aids at the exam are: Tabeller og formler i statistikk, Tapir Forlag, K.Rottmann:Matematisk formelsamling, Calculator Casio fx-82ES PLUS, CITIZEN SR-270X,CITIZEN SR-270X College or HP30S, one yellow A5-sheet with your own handwritten notes. You can get the yellow A5-sheet on the 7th floor in sentralbygg II.

Nov. 21: For those of you (currently Si.Hi., Au.Se., Fr.Lu., An.Ma., An.St.) who plan to take the course as TMA4505 Fordypningsemne, the oral exam will be on December 8 from 11 and onwards. Let me know if you're not listed.

Nov. 11: I'm away on november 15 so no lecture next Tuesday.

Nov. 2: We postpone the lecture tomorrow on Thursday november 3 to Tuesday, november 7. We then start on time series regression and ARCH and GARCH models next week. I'll be available at Nullrommmet on Friday, nov. 4 at 14:15.

Oct. 27: Note that there was a \(\gamma_0\) missing in eq. (3a) in the Lecture summary.

Oct. 14: Problem 1 on project 2 is available.

Oct. 4: We move the computer lab next Friday (Oct. 7) to 13:15-14:15 instead of 14:15-15:00.

Sept. 27: Based on the poll we'll move the exercises to Nullrommet 380A on Fridays at 14:15-15:00 (I'll be present the coming Friday)

Sept. 23: The formula for \(\gamma_0\) for an ARMA(1,2) process shown in yesterdays lecture was incorrect. The correct formula can be written \[\gamma_0 = \frac{\sigma_a^2}{1-\phi_1^2}[1 - 2\phi_1\theta_1 - 2\phi_1\theta_2(\phi_1 - \theta_1) + \theta_1^2 + \theta_2^2].\] It is not necessary to derive lengthy formulas for all \(\gamma_k\) in terms of basic model parameters only. Instead express \(\gamma_1\) in terms of \(\gamma_0\) and so on whenever this makes the presentation more clear.

Sept. 22: Added some additional material to the solution to exercise 4 about how almost any non-invertible model can be made invertible through reparameterization.

Sept. 22: Added point 5-7 to project 1.

Sept. 22: We aim at moving the exercises to the computer lab and need to find a suitable hour each week for everyone. Therefore, please answer this poll.

Sept. 15: A slight correction to problem 1 on project 1 (to simulate an ARMA(1,2) process you may need to consider the joint distribution of \(Z_1,a_1,a_0\) (and not just \(Z_1,a_1\)).

Sept. 15: If you plan to take the course as TMA4505 Fordypningsemne, then send me an email. We aim at doing the oral exam on December 8. You still need to hand in both the projects.

Sept. 15: If you did the project in 2015, you may but are not required to do not hand in a project this year.

Sept. 1: Problem 1 on project 1 has been posted.

First lecture on tuesday, august 23 at 10:15 in R8.

## Preliminary curriculum

The curriculum consists of what is discussed in the lectures and what is covered in the exercises and projects. The topics discussed in the lectures are also covered by the following chapters in "Wei, W.W.S. (2006). Time series analysis. Univariate and multivariate methods, 2nd edn, Pearson Addison Wesley".

- Chapt. 1. All.
- Chapt. 2: All.
- Chapt. 3: All.
- Chapt. 4: All.
- Chapt. 5: All.
- Chapt. 6: 6.1-6.2, 6.4.
- Chapt. 7: 7.1-7.2.1, 7.2.3-7.5.
- Chapt. 8: All.
- Chapt. 15: All.
- Chapt. 18: 18.1-18.2,18.5.

In addition, everything included in Lecture history is part of the curriculum.

## Obligatory projects

Project | Text | Deadline |
---|---|---|

1 | Project 1, points 1-4 (updated sept.15) and 5-8 (added on sept. 22) | Oct. 31, 24:00 |

2 | Project 2, problem 1 (analysis of real data) Project 2, Problem 2 (inference, MLE via the Kalman filter) | Nov. 27, 24:00 |

You may work in groups of one or two students. If you are collaborating with another student, http://www.sharelatex.com, overleaf or similar tools can be recommended for writing the report. Knitr and Rstudio can also be recommended but perhaps only if you work on your own. Signing into sharelatex with your stud.ntnu.no email (ntnu has a subscription) will allow syncing between dropbox and sharelatex (which is convenient when revising figures).

Write your name(s) on the report, not student or candidate numbers.

To solve the problems you may use the computers in the student computer lab of the Department of Mathematical Sciences. If you don't already have a user and physical access to these computer labs you must send a mail to the lecturer and ask for this.

The two projects will in total count 20% of the final grade. Submit your project to Xin Luo.

## Weekly voluntary exercises

Week | Text | Solution |
---|---|---|

35 | Ex. 2.1-2.4 in Wei (hint) | Solution |

36 | Exercise 2 | Solution |

37 | Exercise 3 | Solution |

38 | Exercise 4 | Solution |

39 | Exam December 2013, Problem 1a, 2a,b,c,d | Solution |

40,41,42 | No exercise, work with the project | |

43 | Ex. 4.1, 4.2a, 4.5, 5.2, 5.5 | Solution |

## Course Information

Lecturer: Jarle Tufto. Teaching assistant: Xin Luo

Timetable for lectures and exercises: see here