TIME SERIES ANALYSIS

Four credits

Theory + Exercices 4 credits

I- Course objective

This course provides an introduction to time series modelling

II Prerequisites

Probability theory (TN 402)

Mathematical Statistics (TN0)

III Contents

Chapter 1 Additive models – Statistical modelling

Notions of time series

Linear additive model Parameter estimating

General additive model Estimating the components

Moving average and Exponential filtering

Forecasting

Practice

Chapter 2 Stationary ARMA models

Correlation functions

Spectral density

Forecasting

Chapter 3 ARMA model identification

Preliminary estimators

Consistency Asymptotic Normality

Order model determination

Practice on simulated and genuine time series

Chapter 4 ARMA Parameter estimation Model diagnostics

Maximum likelihood and Least Squares estimates

Asymptotic Normality

Model diagnostics

Residuals analysis and tests

Practice on simulated and genuine time series

Chapter 5 Some classical unstable ARMA

ARIMA and Seasonal ARIMA

Modelling and practice

References

G.E.P Box & G.M. Jenkins Time series analysis Forecasting and Control Holden Day

P.J. Brockwell and R.A Davis Time series: Theory and Methods Springer series in Statistics Springer Verlag New York Berlin Heideberg 1987

G.M. Jenkins & D.G. Watts Spectral analysis and its applications Holden Day

E.J. Hannan Time series 1969 Wiley New York