Course 2021-2022 a.y.


Department of Decision Sciences

Course taught in English
Go to class group/s: 31
CLMG (6 credits - II sem. - OP  |  12 credits 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) - 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) - DSBA (6 credits - II sem. - OP  |  SECS-S/01) - PPA (6 credits - II sem. - OP  |  SECS-S/01) - FIN (6 credits - II sem. - OP  |  SECS-S/01)
Course Director:

Classes: 31 (II sem.)

Suggested background knowledge

Basic notions of Statistics and Probability.

Mission & Content Summary


The analysis of dynamic phenomena is of crucial importance in economic and financial studies. - in fact, in any field of Science. The course aims at providing solid methodological background and data-analysis skills for time series analysis, covering classical as well as modern techniques for non stationary time series, based on state-space models.


  1. Aims of time series analysis and descriptive techniques:
    • Time series decomposition. Exponential smoothing.
  2. Probabilistic models for time series analysis:
    • Time series as a discrete time stochastic process.
    • Stationary processes. Summaries. Estimation of the autocorrelation function.
    • First examples: White noise. Gaussian processes. Random walks.
    • Categorical time series: Markov chains. Inference for Markov processes.
    • Stationary time series: ARMA models (brief review). 
    • Time series with structural breaks: Hidden Markov Models.
  3. State space models for time series analysis:
    • Motivating examples: non-stationary series; stochastic volatility; streaming data.
    • State space models: definition and main properties.
    • Hidden Markov models as state-space models.
    • Dynamic linear models (DLM).                   
    • Filtering, forecasting, smoothing: Kalman filter and Kalman smoother.  
    • Innovation process and model checking.        
    • Maximum likelihood estimation of unknown parameters. 
    • Examples for economic and financial time series. DLMs for trend, seasonality, cycle.
    • Nonlinear regression by DLMs.
    • ARMA models as DLMs.
    • Multivariate time series (dynamic regression (example: term structure of interest rates); seemingly unrelated time series models; factor models).
    • Bayesian inference and forecasting via Markov Chain Monte Carlo (MCMC).
    • Recent developments.                    

Intended Learning Outcomes (ILO)


At the end of the course student will be able to...
  • Explain and describe the main statistical methods for time series analysis.
  • Identify the models suitable for the problems under study; estimate and make forecasts for dynamic systems, both stationary and non-stationary, with an adeguate quantification of uncertainty and risk.  
  • Use R for time series analysis.


At the end of the course student will be able to...
  • Apply and properly interpret the models and methods presented in the course in applications.
  • Use adeguate statistical software (R and main R functions for time series analysis). 
  • Evaluate and justify their analysis on real data.
  • Prepare appropriate reports of their statistical analysis in real data applications. 

Teaching methods

  • Face-to-face lectures
  • Online lectures
  • Exercises (exercises, database, software etc.)
  • Group assignments


  • Online lectures:  a wide set of videolectures on almost all the topics of the course - pretty close to an online, Coursera-like, course.
  • Exercises: lectures in the computer room ('laboratories') on the analysis of real data - or  online "video-lab".  Software: R, freely available at An R-package, 'dlm', has been developed for this course.
  • Students are actively involved in the learning process through individual and team work in periodic assignments.

Assessment methods

  Continuous assessment Partial exams General exam
  • Written individual exam (traditional/online)
  • Group assignment (report, exercise, presentation, project work etc.)


  • There are no partial exams, but there are periodic take-home assignments (individual or group work). Assigments are not mandatory, but strongly encouraged for an active learning. They are not evaluated for the final exam; yet, students who did not deliver the assignments have to answer additional questions on data-analysis with R  in the written proof.
  • A final project on real data analysis (individual or team work) is mandatory and evaluated for the final exam (30%).
  • Written proof (70%; it can be 100% if poorly done) .
  • NOTE: this structure might be slightly changed, if the need occurs, for taking into account the restrictions caused by the covid-19 pandemic.

Teaching materials


  • C. Chatfield, The Analysis of Time Series, Chapman & Hall/CRC, 2004, 6th edition (only a few chapters)
  • G. Petris, S. Petrone, P. Campagnoli, Dynamic Linear Models with R, Springer, New York, 2009.
  • S. Petrone Lecture notes: Introduction to Markov Chains, 2015.
  • S. Petrone. Lecture notes: Hidden Markov Models
  • Lecture notes, data sets, R code, RMarkdown templates etc are made available on the  Bboard of the course.
  • Videolectures and videolabs (online through BBoard)
Last change 11/02/2022 16:36