Insegnamento a.a. 2017-2018



Department of Decision Sciences

Course taught in English

Go to class group/s: 31
CLMG (6 credits - II sem. - OP  |  SECS-S/01) - M (6 credits - II sem. - OP  |  SECS-S/01) - IM (6 credits - II sem. - OP  |  SECS-S/01) - MM (6 credits - II sem. - OP  |  SECS-S/01) - AFC (6 credits - II sem. - OP  |  SECS-S/01) - CLEFIN-FINANCE (6 credits - II sem. - OP  |  SECS-S/01) - CLELI (6 credits - II sem. - OP  |  SECS-S/01) - ACME (6 credits - II sem. - OP  |  SECS-S/01) - DES-ESS (6 credits - II sem. - OP  |  SECS-S/01) - EMIT (6 credits - II sem. - OP  |  SECS-S/01) - GIO (6 credits - II sem. - OP  |  SECS-S/01)
Course Director:

Classes: 31 (II sem.)

Course Objectives

The analysis of dynamic phenomena is extremely important in economic and financial studies. The aim of the course is to provide knowledge of the classical statistical procedures for time series analysis, and of modern techniques based on dynamic linear models (or state-space models). The course intends to provide a solid methodological background and data-analysis skills, with traditional lectures and laboratory-lectures in the computer room, and individual and team work. The software used in the course is R, freely available at A user-friendly R-package, dlm, has been developed for this course, for classical and Bayesian analysis of time series by dinamic linear models.

Course Content Summary

Classical analysis of time series.
  • Descriptive techniques. Decomposition of a time series; trends, seasonality, cycle. Moving average models. Nonparametric techniques.
  • Exponential smoothing. Forecast and model comparison.
  • Stochastic models. Stationary processes.
  • Markov chains (basic notions; inference for Markov processes).
  • ARMA and ARIMA models (basic notions; inference and prediction).
Dynamic linear models for time series analysis.
  • State space models for time series analysis. Examples: non-stationary series; series with structural breaks; series with stochastic volatility; multivariate time series.
  • Hidden Markov models. Dynamic linear models.
  • Estimation, forecasting and control. Kalman filter.
  • Examples and applications to economic and financial time series. Dynamic linear models for trend, seasonality, cycle. Dynamic regression by dlm.
  • Maximum likelihood estimation of unknown parameters.
  • Bayesian inference. Conjugate analysis. Unknown covariance matrices: simple models (discount factors).
  • Analysis of multivariate time series (multivariate ARMA models; dynamic regression - estimation of the term structure of interest rates; factor models; models for macroeconomic variables).
  • Bayesian inference and forecasting via Markov Chain Monte Carlo (MCMC). Recent developments.

Detailed Description of Assessment Methods

There are no partial exams.
Instead, there are:
  • Take-home assignments (about every two weeks).
  • A final project (individual or team work) on the analysis of real data.
The exam consists of an individual written proof and a final project.
Students who do not deliver the assignments have to answer additional questions on the data-analysis in the written proof.
Further details about the exam and suggestions for the final project are given at the beginning of the course and posted on the website of the course. 


  • C. CHATFIELD, The Analysis of Time Series, Chapman & Hall/CRC, 2004, 6th edition.
  • G. PETRIS, S. PETRONE, P. CAMPAGNOLI, Dynamic Linear Models with R, New York, Springer, 2009.
  • S. PETRONE, Lecture Notes: Introduction to Markov Chains, 2015.
  • Teaching material, lecture notes, data sets, examples, R code etc are available on the e-learning space of the course.
  • R is freely available at
Exam textbooks & Online Articles (check availability at the Library)


Suggested but not compulsory: notions of Bayesian inference and Markov chains.
Last change 18/05/2017 11:04