Academic staff

Giuseppe Buccheri,

Referent

Giuseppe Buccheri

Credits

5

Language

English

Class attendance

Free Choice

Location

VERONA

Moodle Seminars 0

Learning objectives

The course covers advanced topics in the analysis of financial time series. In the first part of the course, students will become familiar with ARMA models and linear state-space models. In the second part, some recent developments in research on time-varying parameter time series will be presented, with a particular focus on volatility and dynamic correlation models.

Prerequisites and basic notions

Students are supposed to posses a basic knowledge of calculus, linear algebra and statistics. A basic knowledge of a scientific computing software (Matlab, Python, R) is also required.

Program

Part 1
- Introduction to time series; review of univariate and multivariate statistics; joint and conditional distributions. Markov property; Hilbert spaces and convergence of random variables.
- Weak and strong stationarity; examples of autocorrelation structures; ARMA and VARMA models; Wold decomposition; short and long memory.
- Law of Large Numbers and Central Limit Theorem for dependent data; estimation via Yule-Walker equations. OLS estimation; maximum Likelihood estimation; conditional Maximum Likelihood; Information Criteria.
- Linear state-space models; derivation of the Kalman filter; main properties of the filter; dynamic factor models.
Part 2
- Introductory topics; GARCH-type models; stochastic volatility models; Nonlinear state-space models; 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.

Bibliography

Didactic methods

In-person lectures.

Learning assessment procedures

The final exam consists on 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 the presentation of results.

Assessment

The final evaluation is based on the exam grade.

Criteria for the composition of the final grade

The final grade is given by the evaluation of the presentation.

Scheduled Lessons