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Time Series

Code: 104863 ECTS Credits: 6
2024/2025
Degree Type Year
2503852 Applied Statistics OB 3

Contact

Name:
Coordinació del Grau D'estadística
Email:
coordinacio.grau.estadistica@uab.cat

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.


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

  1. CM09 (Competence) Assess the suitability of the models with the correct use and interpretation of indicators and graphs.
  2. CM09 (Competence) Assess the suitability of the models with the correct use and interpretation of indicators and graphs.
  3. CM10 (Competence) Modify the existing software if required by the statistic model, or create new software, if necessary.
  4. KM12 (Knowledge) Provide the experimental hypotheses of modelling, considering the technical and ethical implications involved.
  5. KM12 (Knowledge) Provide the experimental hypotheses of modelling, considering the technical and ethical implications involved.
  6. KM14 (Knowledge) Identify models to make inferences in processes dependent of time or other ordered variables.
  7. KM14 (Knowledge) Identify models to make inferences in processes dependent of time or other ordered variables.
  8. SM11 (Skill) Analyse the residuals of a statistical model.
  9. SM12 (Skill) Interpret the results obtained to formulate conclusions about the experimental hypotheses.
  10. SM13 (Skill) Compare the degree of adjustment between diverse statistical models.
  11. SM14 (Skill) Use graphs to visualise the fit and suitability of the model.

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. Kalman Filter. 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. Spectral analysis.(*)
  7. Models for non-stationary series: ARCH/GARCH, ARMA with covariates.(*)
  8. Count Time Series: The INAR models.(*)

(*) Optional




Activities and Methodology

Title Hours ECTS Learning Outcomes
Type: Directed      
Practical sessions 26 1.04
Theoretical sessions 26 1.04
Type: Autonomous      
Personal work 60 2.4
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 CM09, KM12, KM14, SM11, SM12, SM13, SM14
Homework (exercises and computer activities) 0,3 8 0.32 CM09, CM10, KM12, KM14, SM11, SM12, SM13, SM14
Mid-term exam 0,3 2 0.08 CM09, KM12, KM14, SM11, SM12, SM13, SM14

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

  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://bibcercador.uab.cat/permalink/34CSUC_UAB/1gfv7p7/alma991002663039706709
  3. 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
  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://bibcercador.uab.cat/permalink/34CSUC_UAB/1eqfv2p/alma991010033559706709
  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.

 

Students can also use Python if they wish.


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 Catalan/Spanish first semester afternoon