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
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.
Pedro José dos Santos Palhinhas Mota
Weekly - 3
Total - 56
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.
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.
The evaluation procedure: one individual home work controled by a Skype interview for 50% a a final exam for 50%.
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;
6.2 Diagnostic tests;
6.4 Practical application in the software.
TP 7. Integrated moving average autoregressive models (ARIMA);
7.1 Nonstationary Processes: ARIMA;
7.3 diagnostic tests;
7.5 Practical application in the software.
Programs where the course is taught: