Academic staff

Giuseppe Buccheri, Lorenzo Frattarolo

Referent

Giuseppe Buccheri

Credits

5

Language

English

Class attendance

Compulsory

Location

VERONA

Moodle Seminars 0

Learning objectives

This course covers advanced topics in the analysis of financial time series. In the first part of the course, students will become familiar with univariate (multivariate) (V)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 (Frattarolo)
- Review of univariate and multivariate statistics; joint and conditional distributions; introduction to time series; martingale and 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.
- GARCH-type models and stochastic volatility models.

Part 2 (Buccheri)
- Linear state-space models; derivation of the Kalman filter; main properties of the filter; dynamic factor 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 and asymptotic theory. Alternative observation-driven specifications.
- 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.

Didactic methods

In person lectures

Learning assessment procedures

The final exam consists on the analysis of a scientific article related to the topics covered within the course. The analysis entails the elaboration and modeling of time-series data and the presentation of results.

Assessment

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Criteria for the composition of the final grade

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Scheduled Lessons