## 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