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| MATH0221-2 | Analysis of time series
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| Duration : | 30h Th, 30h Pr |
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| Credits/ECTS : |
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| Holder(s) : | Paul Gérard |
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| Language : | Langue française |
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| Course contents : | 1 Modelling a time series using the regression method: decomposition of the series into its trend, its seasonal component and its random component (perturbation). Detection of outliers. Correlated perturbations.
2. The theory of moving averages. Kernel of a moving average. Series which are preserved by a moving average. Slutsky-Yule's effect. Usual moving averages: arithmetic, Henderson, Spencer. Moving averages preserving local polynomials, minimizing, under conditions, the variance of the random component. Smoothing capability of a moving average. Program CENSUS X11.
3. Previsions using smoothing procedures: exponential smoothing, Brown's methods, Holt&Winters methods.
4. Second order stationary process. Autocovariance and autocorrelation. Partial autocorrelation and Durbin's algorithm. Spectral density. ARMA(p,q) models, canonical representation. ARIMA and SARIMA models. |
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| Course objective : | To be able to examine a time series, extract its trend and seasonal components. To get accustomed with several methods for modelling and forecasting. |
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| Prerequisites : | Elements of probability theory
Normal linear models theory
Elements on Fourier's analysis |
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| Workshops : | Applications of the various theoreticals methods to observed time series
Exercices about ARMA models and spectral theory. |
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| Written notes : | 1.Séries temporelles et modèles dynamiques. Christian Gourieroux et Alain Monfort. Economica, Collection « Economie et statistiques avancées ».
2.Time series : a biostatistical introduction. P.J.Diggle. Oxford statistical science series. Oxford University Press.
3.Practical time series. Gareth Janack. Arnold. |
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| Assessment : | Oral examination.
Written report about an application. |
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| Contacts : | Paul GERARD
Institut de Mathématique
Grande Traverse, 12
Sart Tilman, 4000 Liège
Couriel: paul.gerard@ulg.ac.be
Tél.: 00-32-(0)43.66.93.84 |
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