Temporal Data Analysis
Code: 104413
ECTS Credits: 6
2024/2025
Degree |
Type |
Year |
2503740 Computational Mathematics and Data Analytics |
OT |
4 |
Teachers
- Anna Lopez Ratera
Teaching groups languages
You can view this information at the end of this document.
Prerequisites
It is advisable to have knowledge on probability, statistical inference and linear models.
Objectives and Contextualisation
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
- CM31 (Competence) Plan studies based on time series with ethical responsibility for real cases.
- CM31 (Competence) Plan studies based on time series with ethical responsibility for real cases.
- CM32 (Competence) Assess the degree of compliance with the requirements necessary to apply each advanced statistical procedure.
- CM32 (Competence) Assess the degree of compliance with the requirements necessary to apply each advanced statistical procedure.
- CM33 (Competence) Draw relevant conclusions from applied problems by applying advanced statistical methods.
- CM33 (Competence) Draw relevant conclusions from applied problems by applying advanced statistical methods.
- CM33 (Competence) Draw relevant conclusions from applied problems by applying advanced statistical methods.
- KM27 (Knowledge) Recognise the advantages and disadvantages of different statistical methodologies when applied to different disciplines.
- KM27 (Knowledge) Recognise the advantages and disadvantages of different statistical methodologies when applied to different disciplines.
- KM28 (Knowledge) Identify the most appropriate modelling for a chronological series.
- KM28 (Knowledge) Identify the most appropriate modelling for a chronological series.
- SM33 (Skill) Use summary graphs of time-varying data.
- SM34 (Skill) Analyse data using the time series model.
- SM35 (Skill) Use statistical software to study time series.
Content
- Introduction. Classical analysis of time series models.
- Stationary Processes. On the concept of stationarity, examples. Simulation.
- 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.
- 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.
- Diagnostic checking and Forecasting. AIC and BIC criteria. Analysis of residuals. Confidence intervals for predictions.
- Models for non-stationary series: ARCH/GARCH, ARMA with covariates.
- Count Time Series: The INAR models.
Unless the requirements enforced by the health authorities demand a prioritization or reduction of these contents.
Activities and Methodology
Title |
Hours |
ECTS |
Learning Outcomes |
Type: Directed |
|
|
|
Practical sessions |
24
|
0.96 |
|
Theoretical sessions |
26
|
1.04 |
|
Type: Autonomous |
|
|
|
Personal work |
62
|
2.48 |
|
Real data analysis |
25
|
1 |
|
During the theoretical lessons (2 H/week) the fundamental results will be presented, and computer exercises will be developed. During the lab hours (with laptop) students will solve real data problems. The programing language used is R.
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
Continous Assessment Activities
Title |
Weighting |
Hours |
ECTS |
Learning Outcomes |
Final Exam |
0,4 |
3
|
0.12 |
CM32, CM33, KM28, SM33, SM34
|
Homework (exercises and computer activities) |
0,3 |
8
|
0.32 |
CM31, CM32, CM33, KM27, KM28, SM33, SM34, SM35
|
Mid-term exam |
0,3 |
2
|
0.08 |
CM33, KM27, KM28, SM33, SM34
|
The subject will be assessed with assignments (exercise assignments, problem checks and/or practicals) and 2 exams. To obtain the weighted grade of continuous assessment you must have a minimum of 3/10 in each of the parts.
Students who have opted for the single assessment modality will have to complete an assessment that will consist of a theory exam, a problem test and the delivery of the first and last practical reports of the course. Assessment of submissions may require an assessment interview with the teacher. The student's grade will be the weighted average of the three previous activities, where the exam will account for 45% of the grade, the test 45% and the assignments 10%.
If the final grade does not reach 5/10, the student has another opportunity to pass the subject through the remedial exam that will be held on the date set by the degree coordinator. In this test you can recover 70% of the grade corresponding to the theory and the problems. The part of internships is not refundable.
Bibliography
- 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
- Brockwell, P.J. and Davis, R.A. (2002). Introduction to Time Series and Forecasting. 2nd edit. Springer. https://bibcercador.uab.cat/permalink/34CSUC_UAB/1gfv7p7/alma991002663039706709
- Cryer, J.D. and Chan, K.S. (2008). Time Series Analysis with Applications to R. 2nd. edit. Springer. https://bibcercador.uab.cat/permalink/34CSUC_UAB/1gfv7p7/alma991008499229706709
- Peña, R.D. A course in time series analysis. https://onlinelibrary-wiley-com.are.uab.cat/doi/book/10.1002/9781118032978
- 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
- Shumway, R.H. and Stoffer, D.S. (2011) Time Series Analysis and its Applications. 3rd. edit. Springer. https://bibcercador.uab.cat/permalink/34CSUC_UAB/1eqfv2p/alma991010033559706709
- Tsay., R.S. (2010). Analysis of Financial Time Series, 3rd Edition, Wiley.
Software
R Core Team (2021). 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.
Language list
Name |
Group |
Language |
Semester |
Turn |
(PLAB) Practical laboratories |
1 |
Catalan |
first semester |
afternoon |
(PLAB) Practical laboratories |
2 |
Catalan |
first semester |
afternoon |
(TE) Theory |
1 |
Spanish |
first semester |
afternoon |