Time Series

Information

Teachers: Isabel Pereira

Duration: One semester

Work hours: 162

Contact hours: 45

ECTS: 6

Scientific area: Mathematics

Objectives

The objectives of this course are to provide students with:

  • the knowledge and basic tools to acquire the skills that allow them to describe, analyze, interpret and predict the future evolution of univariate time series;
  • the necessary bases for the practical modeling of real data;
  • the ability to use the R program to model and analyze time series (economic and financial).

Learning Outcomes

Students should be able to describe, analyze, interpret, model and predict the future evolution of univariate time series and use the R program for time series modeling.

Requirements

Knowledge of probability theory and statistics and basics of stochastic processes.

Grading

Exam and practical assignments.

Methodology

Theoretical-practical classes with exposition of theory, proposals for solving exercises and use of the R software.

Syllabus

  • Introduction: time series definition, examples and objectives
  • Stochastic Processes: definition, specification of stochastic process.
  • Stationary Linear Processes: AR, MA, ARMA, seasonal.
  • Non-Stationary Linear Processes: non-stationarity in mean and in variance; integrated processes.
  • Time Series Modeling: identification, estimation and diagnosis; template selection criteria
  • Forecast: in AR, MA and ARMA representations; forecast updates; confidence intervals; other forecasting methods.
  • Additional topics: time series analysis with outliers, influencers, and missing values; long memory processes; some non-linear models; exponential smoothing methods.

Recommended reading

  • Brockell, P.J. e Davis, R.A. (1996) Introduction to Time Series and Forecasting. Springer-Verlag, New-York.
  • Chan, N.H. (2010) Time Series: Applications to Finance with R and S-Plus. 2nd Edition. Wiley Series in Probability and Statistics. John Wiley and Sons.
  • Hyndman, R., Koehler, R., Ord, A.B. e Snyder, R.D. (2011) Forecasting with Exponential Smoothing: the State Space Approach, Springer.
  • Hyndman, R. e Athanasopoulos, G. (2013) Forecasting: Principles and Practice, OTexts.
  • Murteira, B., Muller, D.A. e Turkman, K.F., (1993) Análise de Sucessões Cronológica. McGraw-Hill, Lisboa.
  • Tsay, R.S. (2010) . Analysis of Financial Time Series. Third Edition. John Wiley and Sons.
  • Shumway, R.H e Stoffer, D.S. (2011) Time series Analysis and Its Applications: With R Examples, Springer.