Tópicos Avançados em Estatística: Séries Temporais


In the end, the student should be able to:
1. Know the concept and give examples of time series; 
2. Know the concept of stationary time series, with tendency or seasonality; 
3. Know the concepts and calculate the function of autocovariance, 
autocorrelation and partial autocorrelation of a time series; 
4. Know how to use seasonality or trend removal methods in order to obtain 
a stationary series; 
5. Apply a moving average; 
6. Decompose a time series; 
7. Know the basic steps for modeling a time series; 
8. Know how to interpret the autocorrelation function of a time series; 
9. Apply tests for the absence of autocorrelation; 
10. Know the concept of stochastic process; 
11. Know the concept of stationary autoregressive (AR), moving average (MA) 
and autoregressive moving average (ARMA) processes; 
12. Know the concept of autoregressive integrated moving average non-stationary 
processes (ARIMA); 
13. Know how to adjust an AR, MA, ARMA and ARIMA model using the software; 
14. Perform diagnostic verification for previous models; 
15. Make prediction using the previous models.

General characterization





Responsible teacher

Pedro José dos Santos Palhinhas Mota


Weekly - 3

Total - 56

Teaching language



Basic knowledge of Probability and Statistics.


  • Box GEP, Jenkins GM, Reinsel GC. Time series analysis: forecasting and control. 3rd ed. Englewood Cliffs, NJ: Prentice Hall, 1994.

  • Brockwell PJ, Davis RA. Time series: theory and methods. 2nd ed. New York: Springer-Verlag, 1991.

  • Diggle P. Time series: a biostatistical introduction. Oxford, United Kingdom: Oxford University Press, 1989.

  • Gonçalves E, Lopes NM. Séries temporais: Modelações lineares e não lineares. Minicurso SPE, 2008.

  • Helfenstein U. Box-Jenkins modelling in medical research. Stat Methods Med Res 1996; 5:3–22.

  • Müller D. Processos Estocásticos e Aplicações. Almedina, 2007.

  • Murteira BJF, Muller D, Turkman KF. Análise de Sucessões Cronológicas, McGraw-Hill, Lisboa, 1993.

  • Zeger SL, Irizarry R, Peng RD. On time series analysis of public health and biomedical data. Annu Rev Public Health 2006; 27:57–79.

Teaching method

This course is given using e-learning. Besides the usual tools (on-line help, email, chat, digital material) a set of video recordings with motivation, introductory explanations and development of problem solving techniques is made available to the students. The digital material contains course notes and a set of problems with solutions.

Evaluation method

The evaluation procedure: one individual home work controled by a Skype interview for 50% a a final exam for 50%.

Subject matter

TP 1 - Introduction   
1.1 Time Series: definition and objectives of the analysis; 
1.2 Examples of time series; 
1.3 Concepts of autocovariance and autocorrelation; 
1.4 Stationary Series. 
1.5 Practical application in software   

TP 2 - Series Decomposition   
2.1 Components of a time series; 
2.2 Decomposition models; 
2.3 Trend extraction and seasonal component models; 
2.4 Regression, Moving Averages and Differences; 
2.5 Seasonal decomposition; 
2.6 Practical application in the software.   

TP 3 - General approach to modeling   
3.1 Basic steps for modeling a time series; 
3.2 Graph analysis; 
3.3 Normality tests; 
3.4 Observation of the autocorrelation and partial autocorrelation function; 
3.5 Ljung-Box test for absence of autocorrelation; 
3.6 Practical application in the software.   

TP 4 - autoregressive models (AR);   
4.1 Stationary processes: AR; 
4.2 Autocorrelation and partial autocorrelation functions; 
4.3 Practical application in the software.     

TP 5 - Moving Average Autoregressive Models (ARMA)   
5.1 Stationary processes: MA; 
5.2 Stationary processes: ARMA; 
5.3 Autocorrelation and partial autocorrelation functions; 
5.4 Practical application in the software.       

TP 6 - Modeling and prediction in ARMA models;   
6.1 Estimation; 
6.2 Diagnostic tests; 
6.3 Forecasting; 
6.4 Practical application in the software.     

TP 7. Integrated moving average autoregressive models (ARIMA);   
7.1 Nonstationary Processes: ARIMA; 
7.2 Estimation; 
7.3 diagnostic tests; 
7.4 forecasting; 
7.5 Practical application in the software.


Programs where the course is taught: