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Statistical Modelling II
Courses Doctor’s Degree in Applied Mathematics and Modelling
Cod: 23033
Department: DCET
ECTS: 10
Scientific area: Statistics
Total working hours: 260
Total contact time: 20

This learning unit (LU) to provide knowledge and skills in some particular statistical modeling methods used in the study of time series. The CU addresses two essential perspectives, the study within the time domain using the extension of linear models, and the study in the frequency domain with its fundamental tools.

Statistical modelling
Time series

- Know the concepts and methods of modelling a univariate time series that were studied and perform some applications with supporting statistical software;
- Be able to identify the advantages and disadvantages of one type of modeling,and recognize the complementarities;
- Have acquired familiarity with the types of modeling and derivation of significance tests studied, enabling him/her to make the most suitable choice to a specific context and purpose and investigate new methodologies / testing or improving existing methodologies.

  1. Review of Linear Models: Least Squares; Gauss-Markov theorem, confidence intervals, and prediction; General Linear Model; Generalized Least Squares and Maximum Likelihood; residual analysis.
  2. Time series in time domain (discrete), time series and dependent observations. Series decomposition and estimation of components, types of stochastic processes, AR(I)MAmodels; stationarity and invertibility; seasonal and non-stationary models; functions auto-covariance and autocorrelation functions, Gaussian processes. Diagnosis; hypothesis testing. Analysis of Stationarity. Prediction in linear models and reference to other techniques.. Examples studied using the software.
  3. Time series in the frequency domain. Spectral Density; Fourier Transform; the periodogram. Other possible topics: Wavelets, Independent Component Analysis; time series and artificial neural networks.
  4. Time series and artificial neural networks: definition and structure of a neural networks; types of neural networks (back propagation, RBF, dynamic Bayesian, predictive modular); the use of neural networks for the estimation and forecasting of time series.

• Woodward, Gray, Elliott: Applied Time Series Analysis, CRC Press, 2011
• Bloomfield: Fourier Analysis of Time Series: An Introduction, 2nd ed, Wiley, 2000
• Pedrycz, Chen: Time Series Analysis, Modeling and Applications: A Computational Intelligence Perspective, Springer, 2012

E-learning

Evaluation is made on individual basis and it involves the coexistence of two modes: continuous assessment (60%) and final evaluation (40%). Further information is detailed in the Learning Agreement of the course unit.