# Tópicos Avançados em Estatística: Séries Temporais

## Objectives

`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

12022

4.0

##### Responsible teacher

Pedro José dos Santos Palhinhas Mota

Weekly - 3

Total - 56

Português

### Prerequisites

Basic knowledge of Probability and Statistics.

### Bibliography

• 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

Programs where the course is taught: