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 seires. Stochastic processes: definition, characterization (Kolmogorov theorem) and properties: stationarity, invertibilità, ergodicity. Examples: white noise, iid, Gaussian processes. 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 partila autocovariance and autocorrelation functions; spectral anlaysis in the frequency domain.

Modelling. Finite approximation of infinit order AR and infinit order MA processes: AR(p), MA(q), ARMA(p,q) processes. Seasonal ARIMA(p,d,q) models for nonstationary homogeneus linear processes. Box-Jenkins procedure for the identification, estimation, diagnostic and forecasting of a SARIMA processes. Implementation trhough the software SPSS. Analyes of real time series.

Decomposition. Identification and estimation of the trend-cycle, seasonality and irregular components. Deterministic and stochastic models. Parametrc and non parametric methods. Weighted moving averages and their properties. The X11ARIMA/88 method: statistical foundations and decomposition of real time series through the X11ARIMA software.

Nonlinear time series analysis: introduction toARCH and GARCH processes.

Readings/Bibliography

Textbooks:

BOX, G.E.P., JENKINS, G.M. (1970): Time Series Analysis: Forecasting and Control, Holden Day, San Francisco, U.S.A (second edition, 1976).

P.J. BROCKWELL, R.A. DAVIS, Time series: theory and methods. Springer-Verlag 1991.

Other references:

Gardini A., Cavaliere G., Costa M., Fanelli L., Paruolo P. (2000) Econometria, Vol. I, Franco Angeli.

- chapter 5, sections 5.1, 5.2

Hamilton J.D. (1994), Time series analysis, Princeton University Press.

- chapter 6

Cont R. (2001), “Empirical properties of asset returns: stylized facts and statistical issues”, Quantitative Finance, 1, 223-236.

Teaching methods

Classroom lessons and laboratory exercises (software: SPSS and X11ARIMA).

Assessment methods

Written, practical (laboratory) and oral examinantion.

Teaching tools

Lessons can be found on the teacher web-site.

Links to further information

http://www2.stat.unibo.it/luati

Office hours

See the website of Alessandra Luati

See the website of Fedele Pasquale Greco