Course 2024-2025 a.y.

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.                    

• 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.

• 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. 

• Lectures
• Practical Exercises
• Collaborative Works / Assignments

• Online lectures: We might have a few online lectures held by an international  expert, on advanced models and applications. (Moreover, as auxiliary teaching material: I have a wide set of videolectures on almost all the topics of the course - pretty close to an online, Coursera-like, course. Some of these might be made available, according to Bocconi policy).
• Exercises: lectures ('laboratories') on your laptop on the analysis of real data - or  online "video-lab".  Software: R, freely available at www.r-project.org. 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.

There are no partial exams, but there are periodic assignments (individual or group work). Assignments are strongly encouraged for students' active learning. They are aimed at consolidating students' understanding of the theory and methods and of their motivating applications; their actual implementation in real data analysis; and, also importantly, students' presentation skills. Assignments are mostly take-home work but may include in-class individual tests. The assignments are not mandatory; yet, students who did not deliver the assignments have to answer additional questions on data-analysis with R in the written proof. Moreover, if the assignments are well done, they may be valued up to 3 extra points on the final project (see below), or up to 1 extra point on the written proof in the case of an in-class individual test on the theory.

• 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.
• 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) MIGHT be made available, in the respect of Bocconi policy.