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Time Series

Code: 100124
Credits: 6
2026/2027
Degree programme Type Course
Mathematics OP 4

Contact lecturer

Name :
David Moriña Soler
Email :
david.morina@uab.cat

Group languages

You can consult this information at the end of the document.

Prerequisites

It is advisable to have knowledge on probability, statistical inference and linear models.

Objectives

This course aims to introduce students to time series models and their applications. A time series is a set of observations of a random phenomenon evolving over time (or any other ordered magnitude). Time series appear in many fields of application. Therefore, their analysis and the modelling of the underlying random phenomena are of crucial theoretical and applied importance. The ultimate goal is the modelling of the mechanism that generates the data, performing model diagnostics, and predicting future values.

Learning outcomes

  1. Effectively use bibliographies and electronic resources to obtain information.
  2. Students must have and understand knowledge of an area of study built on the basis of general secondary education, and while it relies on some advanced textbooks it also includes some aspects coming from the forefront of its field of study.
  3. Students must be capable of applying their knowledge to their work or vocation in a professional way and they should have building arguments and problem resolution skills within their area of study.
  4. Develop critical thinking and reasoning and know how to communicate it effectively, both in one's own languages and in a third language.
  5. Students must be capable of collecting and interpreting relevant data (usually within their area of study) in order to make statements that reflect social, scientific or ethical relevant issues.
  6. Students must be capable of communicating information, ideas, problems and solutions to both specialised and non-specialised audiences.
  7. Students must develop the necessary learning skills to undertake further training with a high degree of autonomy.
  8. Actively demonstrate high concern for quality when defending or presenting the conclusions of one's work.
  9. Have the capacity to devise and construct models and validate the same.
  10. Data analysis.
  11. Recognise the different types of sampling.
  12. Determine the size of the sample and establish a sampling strategy for proportion comparison studies.
  13. Determine the size of the sample and establish a sampling strategy for comparison of means studies.
  14. Determine the size of the sample and establish a sampling strategy for special comparisons.
  15. Characterise homogenous groups of individuals by means of multivariate analysis.
  16. Devise a study on the basis of multivariate and/or data mining methodologies to solve a problem that is contextualised in the experimental reality.
  17. Recognise the need to employ multivariate rather than bivariate methods.
  18. Design experiments.
  19. Identify relationships or associations.
  20. Interpret results using statistical models.
  21. Use quantitative thinking and reasoning.
  22. Identify the relevant information in order to solve a problem.
  23. Filter and store information on digital supports.
  24. Validate and manage information for statistical treatment.
  25. Identify the stages of problems that require advanced technologies.
  26. Use multivariate data summary indexes, time series and all other advanced techniques.
  27. Use graphs to summarise multivariate data and show dynamical pictures.
  28. Represent data graphically.
  29. Design, program and implant statistical packages.
  30. Devise predictions and scenarios.
  31. Use statistical programs to manage databases.
  32. Use statistical programs to obtain summarised indexes of study variables.
  33. Use statistical programs to calculate sample sizes.
  34. Use statistical programs for different multivariate analysis methods.
  35. Take sex- or gender-based inequalities into consideration when operating within one's own area of knowledge.

Contents


  1. Introduction. Classical analysis of time series models.

  2. Stationary Processes. On the concept of stationarity, examples. Simulation.

  3. Linear models. MA(q) and AR(p). Correlograms. Yule-Walker equations. The difference operator. Relationship between MA snd AR models. The autocorrelation and partial autocorrelation functions.

  4. ARIMA Models. The ARMA(p,q) model. Parameter estimation: method of moments, MLE, unconditional and conditional least squares. The ARIMA(p,d,q) and SARIMA models. The Box-Jenkins method. Segmentation.

  5. Diagnostic checking and Forecasting. AIC and BIC criteria. Analysis of residuals. Confidence intervals for predictions.

  6. Models for non-stationary series: ARCH/GARCH, ARMA with covariates.

  7. Count Time Series: The INAR models.




Learning activities and methodology

Title Hours ECTS Learning outcomes
Practical sessions 26 1.04 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35
Personal work 60 2.4 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35
Theoretical sessions 26 1.04 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35
Real data analysis 25 1 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35

During the two weekly theoretical hours, the fundamental theoretical results will be presented, and computer-based exercises and problems will be solved. During the two weekly hours of computer-based practical sessions, R will be used to apply the models studied in the theoretical classes.

The gender perspective in teaching goes beyond the content of the courses, as it also involves reviewing teaching methodologies and interactions between students and teaching staff, both inside and outside the classroom. In this regard, participatory teaching methodologies, which foster an egalitarian and less hierarchical classroom environment, avoid gender-stereotyped examples and sexist language, and aim to develop critical thinking and respect for the diversity and plurality of ideas, people and situations, are generally more favourable to the integration and full participation of female students in the classroom. For this reason, their effective implementation will be sought in this course.

In this course, the use of Artificial Intelligence (AI) technologies is permitted as an integral part of the development of coursework, provided that the final result reflects a significant contribution by the student in terms of analysis and personal reflection. Students must clearly identify which parts have been generated using this technology, specify the tools used, and include a critical reflection on how these tools have influenced the process and the final outcome of the activity. Failure to be transparent about the use of AI will be considered a breach of academic integrity and may result in a penalty in the mark for the activity, or more serious sanctions in severe cases.

Annotation: within the schedule set by the centre or degree programme, 15 minutes of one class will be reserved for students to evaluate their lecturers and their courses or modules through questionnaires.

Assessment

Continuous assessment activities

Title Weight Hours ECTS Learning outcomes
Homework (exercises and computer activities) 0,3 8 0.32 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35
Mid-term exam 0,3 2 0.08 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35
Final Exam 0,4 3 0.12 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35

In the continuous assessment modality, the course will be assessed through coursework submissions (submission of exercises, problem-solving tests and/or practical assignments) and two exams. In order to obtain the weighted continuous assessment mark, students must achieve a minimum score of 3/10 in each of the components.

Students who have opted for the single assessment modality must complete an assessment consisting of a theory exam, a problem-solving test, and the submission of the reports corresponding to the first and last practical sessions of the course. The assessment of these submissions may require an evaluation interview with the lecturer. The student’s final mark will be the weighted average of the three activities mentioned above, with the exam accounting for 45% of the mark, the test for 45%, and the submissions for 10%.

If the final mark does not reach 5, the student will have another opportunity to pass the course through the resit exam, which will take place on the date set by the degree coordination. In this exam, students may recover 70% of the mark corresponding to theory and problem-solving. The practical assignment submission component is not recoverable.

Any irregularity committed during an assessment activity — academic fraud, plagiarism, or misuse of AI, unless such use is expressly authorised in the course guide — that may lead to a significant variation in the mark will result in that assessment activity being graded with a 0. If the course guide establishes that, in order to pass the course, it is an essential requirement to have obtained a minimum mark in that assessment activity, or if several irregularities occur in assessment activities for the same course, the final mark for the course will be 0. In addition, disciplinary proceedings may be initiated against any student who commits any of these irregularities.

Bibliography

  1. Bisegard, S. (2011). Time Series Analysis and Forecasting By Example. John Wiley & Sons, Inc., Hoboken, New Jersey. https://onlinelibrary-wiley-com.are.uab.cat/doi/pdf/10.1002/9781118056943
  2. Brockwell, P.J. and Davis, R.A. (2002). Introduction to Time Series and Forecasting. 2nd edit. Springer. https://cataleg.uab.cat/iii/encore/record/C__Rb1671241__Sa%3A%28Brockwell%29%20t%3A%28time%20series%29__P0%2C3__Orightresult__U__X4?lang=spi&suite=def
  3. Cryer, J.D. and Chan, K.S. (2008). Time Series Analysis with Applications to R. 2nd. edit. Springer. https://cataleg.uab.cat/iii/encore/record/C__Rb2027637__Sa%3A%28Cryer%29%20t%3A%28time%20series%29__P0%2C1__Orightresult__U__X4?lang=spi&suite=def
  4. Peña, R.D. A course in time series analysis. https://onlinelibrary-wiley-com.are.uab.cat/doi/book/10.1002/9781118032978
  5. Peña, D., Tiao, G.C., and Tsay, R.S. (2001). A Course in Time Series Analysis. John Wiley & Sons, Inc. https://onlinelibrary-wiley-com.are.uab.cat/doi/book/10.1002/9781118032978
  6. Shumway, R.H. and Stoffer, D.S. (2011) Time Series Analysis and its Applications. 3rd. edit. Springer. https://cataleg.uab.cat/iii/encore/record/C__Rb1784344__Sa%3A%28shumway%29%20t%3A%28time%20series%29__P0%2C2__Orightresult__U__X4?lang=spi&suite=def
  7. Tsay., R.S. (2010). Analysis of Financial Time Series, 3rd Edition, Wiley. 

Software

R Core Team. R: A language and environment for statistical computing. R
  Foundation for Statistical Computing, Vienna, Austria. URL
  https://www.R-project.org/.

We shall use several R libraries, including  forecast, TSA, TSeries, quantmod, fgarch, tscount.

Course groups and languages

The information provided is provisional until November 30. After this date, you will be able to consult the language of each group through this link. To access the information, you will need to enter the course CODE