UE Time series analysis

Diplômes intégrant cet élément pédagogique :

Descriptif

Time Series Characteristics: Some Time Series Data; Time Series

Models; Measures of Dependence; Stationary Time Series; Estima- tion of Correlation.

Time Series Regression: Classical Regression for Time Series; Ex- ploratory Data Analysis; Smoothing Time Series.

ARIMA Models: Autoregressive Moving Average Models; Autocor- relation and Partial Autocorrelation; Estimation; Least Squares Es- timation; Forecasting; Maximum Likelihood Estimation; Integrated Models; Building ARIMA Models Regression with Autocorrelated Er- rors; Seasonal ARIMA Models.

Some Additional Topics: (Depending on the time left.) GARCH Models; Transfer function models; Intervention analysis; Long Mem- ory and Fractional Differencing; Unit Root Testing.

In parallel with the introduction of statistical concepts, R commonly                         used procedures are introduced. A special attention will be given to astsa packages developed by David Stoffer, see Shumway and Stoffer (2011) and TSA developed by Kung-Sik Chan and Brian Ripley, see Cryer and Chan (2008) .

 

Evaluation :

There will be a final written exam. Duration: 2 hours. Autho- rized documents: handwritten summary on two two-sided single A4 sheets and a copy of the course slides available on the website. Prohibited materials: other documents. Equipment: Authorized material: calculator; Prohibited materials: mobile phone / com- puter; think about spare batteries.

Pré-requis

Shumway and Stoffer (2016) state that “the prerequisites are an understanding of linear regression and some basic probability” andstatistic “skills . . .  It also assumes general math skills at the high school level (trigonometry, complex numbers, polynomials, calculus, and so on).

Compétences visées

At the end of the course, the student will be able to analyse and model time series, not necessarily stationary, by proposing a model and proceed to the estimation of parameters using specific R pack- ages and validate the proposed model. He will also be able to pro- duce forecasts in terms of prediction intervals.

Bibliographie

Abraham, B. and J. Ledolter (1983). Statistical Methods for Fore- casting (1 ed.). Wiley Series in Probability and Statistics. New York: Wiley.

Brockwell, P. J. and R. A. Davis (1996). Introduction to Time Series and Forecasting (1 ed.). Springer series in statistics. New York: Springer.

Cowpertwait, P. S. P. and A. Metcalfe (2009). Introductory Time Series with R. Springer Series in Statistics. Springer.

Cryer, J. D. and K.-S. Chan (2008). Time Series Analysis: With Applications in R (2 ed.). Springer texts in statistics. New York: Springer.

Diggle, P. J. (1996). Time Series: A Biostatistical Introduction (1 ed.). Oxford Statistical Science Series, No. 5. New York: Oxford University Press.

Gouriéroux, C. and A. Montfort (2000). Séries temporelles et modèles dynamiques. École nationale de la statistique et de l’administration économique et Centre d’étude des programmes économiques. Paris: Economica.

Makridakis, S. G., S. C. Wheelwright, and R. J. Hyndman (1997).

Forecasting: Methods and Applications (3 ed.). New York: Wiley.

Pankratz, A. (1991). Forecasting with Dynamic Regression Models (1 ed.). Wiley series in probability and mathematical statistics. New York: Wiley-Interscience.

Shumway, R. H. and D. S. Stoffer (2011). Time Series Analysis and Its Applications: With R Examples (3 ed.). Springer texts in statistics. New York: Springer.

Shumway, R. H. and D. S. Stoffer (2016). Time Series Analysis and Its Applications: using R statistical package. Pittsburg: Free Dog Publishing.

Informations complémentaires

Méthode d'enseignement : En présence
Langue(s) : Anglais