12511 - Time Series Analysis

Learning outcomes

The aim of the course is to provide time series theory and methods such that it is possible to attend advanced time series courses and to perform real data analysis in a critical way.

Course contents

Introduction. Definition of time series

Stochastic processes. Definition, characterization (Kolmogorov theorem) and properties: stationarity, invertibilità, ergodicity. Linear processes and Wold theorem. Backshift operator, difference operator and their properties. Polinomyals in the backshift operator. Infinit order AR and MA representations of linear stochastic processes. Global and partial autocovariance and autocorrelation functions.

Modelling. Finite approximation of infinit order AR and infinit order MA processes: AR(p), MA(q), ARMA(p,q) processes. ARIMA(p,d,q) models for nonstationary homogeneus linear processes. SARIMA(p,d,q)(P,D,Q) models for seasonal nonstationary homogeneus linear processes. Box-Jenkins procedure for the identification, estimation, diagnostic of a SARIMA processe. Analysis of real time series.

Decomposition. Identification and estimation of the trend-cycle, seasonality and irregular components. Deterministic and stochastic models. Parametric and non parametric methods.

Readings/Bibliography

E.B. Dagum, Analisi delle serie storiche. Modellistica, previsione e scomposizione. Springer-Verlag Italia, Milano, 2001.

Teaching methods

Lectures and practicals

Assessment methods

The final exam consists of a written and an oral part

Office hours

See the website of Marilena Pillati