Financial Time Series (2023/2024)

Course code
cod wi: dt001091
Name of lecturers
Giuseppe Buccheri, Francesca Rossi
Giuseppe Buccheri
Number of ECTS credits allocated
Academic sector
Language of instruction
Anno accademico 2023/2024 Dottorato di Ricerca dal Oct 1, 2023 al Sep 30, 2024.

Lesson timetable

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Learning outcomes

This is a graduate course on recent topics in Financial Time Series.\ In the first part of the course students will familiarize with the fundamental notions of time series analysis, with a particular emphasis on ARMA models.\ In the second part, some recent advances in financial time series models and volatility forecasting will be presented.


Part 1
Lecturer: Francesca Rossi (10 hours)
- Introduction to time series; review of univariate statistics; tests for serial correlation; review of multivariate statistics; conditional distributions; the Markov property.
- Weak and strong stationarity; examples of autocorrelation structures; AR(1) and AR(2) models; MA(1) and MA(2) models; ARMA(1,1) models; ARMA(p,q) models; Wold decomposition.
- Law of Large Numbers and Central Limit Theorem for dependent data; estimation via Yule-Walker equations; OLS estimation; Maximum Likelihood estimation; Conditional Maximum Likelihood principle; Information Criteria.
Part 2
Lecturer: Giuseppe Buccheri (10 hours)
- Introductory topics. GARCH-type models, stochastic volatility models, Kalman filter. Cox classification of parameter-driven versus observation-driven models.
- Score-driven models as observation-driven models. Univariate score-driven volatility models based on Student-t and GED distributions. Scaling factors and link functions. Stationarity and ergodicity.
- DCC and dynamic correlation models based on the Student-t distribution. ``DRD" decomposition of the covariance matrix, (un)identifiability of static parameters, hyperspherical coordinates. Comparison with DCC.
- Realized measures. Univariate and multivariate score-driven models for realized measures. Estimation errors and curse-of-dimensionality. Two-step approaches and comparison with HAR-DRD.

Reference books

See the teaching bibliography

Assessment methods and criteria

The final exam consists of a written examination covering the topics of Part 1, and the analysis of a scientific article related to Part 2 of the course. The analysis entails the elaboration and modeling of time-series data and writing a report.