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2022/2023

Time Series

Code: 104863 ECTS Credits: 6
Degree Type Year Semester
2503852 Applied Statistics OB 3 1

Contact

Name:
Amanda Fernandez Fontelo
Email:
amanda.fernandez@uab.cat

Use of Languages

Principal working language:
spanish (spa)
Some groups entirely in English:
No
Some groups entirely in Catalan:
No
Some groups entirely in Spanish:
No

Other comments on languages

Class material (slides and practical excercises) will be in english, spanish and/or catalan.

Teachers

Anna Lopez Ratera

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.

Competences

  • Analyse data using statistical methods and techniques, working with data of different types.
  • Correctly use a wide range of statistical software and programming languages, choosing the best one for each analysis, and adapting it to new necessities.
  • Critically and rigorously assess one's own work as well as that of others.
  • Design a statistical or operational research study to solve a real problem.
  • Formulate statistical hypotheses and develop strategies to confirm or refute them.
  • Make efficient use of the literature and digital resources to obtain information.
  • Select and apply the most suitable procedures for statistical modelling and analysis of complex data.
  • Select statistical models or techniques for application in studies and real-world problems, and know the tools for validating them.
  • 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.
  • 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.
  • Students must be capable of communicating information, ideas, problems and solutions to both specialised and non-specialised audiences.
  • Summarise and discover behaviour patterns in data exploration.
  • Use quality criteria to critically assess the work done.

Learning Outcomes

  1. Analyse data through inference techniques using statistical software.
  2. Analyse data using models of time series.
  3. Analyse the residuals of a statistical model.
  4. Critically assess the work done on the basis of quality criteria.
  5. Establish the experimental hypotheses of modelling.
  6. Identify response distributions with the analysis of residuals.
  7. Identify the stages in problems of modelling.
  8. Identify the statistical assumptions associated with each advanced procedure.
  9. Make effective use of references and electronic resources to obtain information.
  10. Make slight modifications to existing software if required by the statistical model proposed.
  11. Measure the degree of fit of a statistical model.
  12. Reappraise one's own ideas and those of others through rigorous, critical reflection.
  13. Recognise the need to use models for non-independent errors.
  14. 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.
  15. 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.
  16. Students must be capable of communicating information, ideas, problems and solutions to both specialised and non-specialised audiences.
  17. Use graphics to display the fit and applicability of the model.
  18. Use statistical inference as an instrument of prognosis and prediction in time series.
  19. Use summary graphs for multivariate data and temporal evolution data.
  20. Validate the models used through suitable inference techniques.

Content

  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.

Unless the requirements enforced by the health authorities demand a prioritization or reduction of these contents.



Methodology

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.

The proposed teaching methodology may experience some modifications depending on the restrictions on face-to-face activities enforced by health authorities

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.

Activities

Title Hours ECTS Learning Outcomes
Type: Directed      
Practical sessions 26 1.04 2, 1, 3, 12, 4, 5, 19, 17, 6, 7, 8, 11, 10, 16, 14, 15, 13, 18, 20
Theoretical sessions 26 1.04 2, 1, 3, 5, 19, 17, 6, 7, 8, 11, 14, 15, 13, 9, 18, 20
Type: Autonomous      
Personal work 60 2.4 2, 1, 3, 12, 4, 5, 19, 17, 6, 7, 8, 11, 10, 16, 14, 15, 13, 9, 18, 20
Real data analysis 25 1 2, 1, 3, 12, 4, 5, 19, 17, 6, 7, 8, 11, 10, 16, 14, 15, 13, 9, 18, 20

Assessment

During the course, students must handle computer labs. There will be mid-term and final exams that will include both theoretical and practical questions. To be eligible for the resit exam, you must get a minimum of 3/10 in practice and theory.

Student’s assessment may experience some modifications depending on the restrictions on face-to-face activities enforced by health authorities

Assessment Activities

Title Weighting Hours ECTS Learning Outcomes
Final Exam 0,4 3 0.12 2, 1, 3, 5, 6, 7, 8, 11, 16, 13, 18, 20
Homework (exercises and computer activities) 0,3 8 0.32 2, 1, 3, 12, 4, 5, 19, 17, 6, 7, 8, 11, 10, 16, 14, 15, 13, 9, 18, 20
Mid-term exam 0,3 2 0.08 2, 1, 3, 5, 6, 7, 8, 11, 16, 13, 18, 20

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 (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.