85004 - Statistical Tools for Forecasting

Course Unit Page

Academic Year 2018/2019

Learning outcomes

This course will provide students with a basic knowledge of statistical techniques often used for forecasting. These methods include causal models employing linear regression and time series analysis estimation approaches. At the end of the course, the student will be able to select the most appropriate predictive technique on the basis of (a) the nature of the research question or the problem at hand, and (b) the kind of data available, i.e. demographic, economic, social, etc.

Course contents

- Real time series. Examples and characterization.

-  Stochastic processes. Definition and chacterization. Delay and difference operators. Strong and weak stationarity. Invertibility and ergodicity. Linear processes and Wold's theorem. Global and partial autocovariance and autocorrelation functions.

- Time series models. Definition and characterization of the following processes: white noise, moving average of order q (MA(q)), autoregressive of order p (AR(p)), autoregressive moving average ARMA(p,q). Seasonality and trend: linear homogenous non-stationary processes (ARIMA(p,d,q)).

- Forecasting.  Expected conditioned value and forecast error. Examples on ARMA processes.

- Real time series analysis. Box and Jenkins procedure: preliminary analysis, model identification, model validation, forecast.


M. Box-Steffensmeier, John R. Freeman, Matthew P. Hitt, Jon C. W. Pevehouse (2014). Time Series Analysis for the Social Sciences. Cambridge University Press. Book DOI: http://http//dx.doi.org/10.1017/CBO9781139025287

Brockwell P.J. and Davis R.A. (2002). Introduction to Time Series and Forecasting. Springer

Teaching methods

Lectures, class exercises, laboratory on R.

Assessment methods

The assessment will result in a written exam composed by theoretical questions (concerning stochastic processes and time series models), and practical questions (concerning real time series analysis). During the course, periodical tests will be provided in order to assess the effectiveness of learning in itinere.

Teaching tools

In addition to textbooks, notes, schemas and relevant papers will be provided by the teacher on Alm@DL at 


Links to further information


Office hours

See the website of Matteo Farnè