NON LINEAR MODELS AND FINANCIAL ECONOMETRICS

This course belongs to the fundamentals teaching activities of the course called "Economia e Finanza". In line with the educational objectives of the course, this activity aims to present the main mathematical and statistical tools necessary for the analysis of economic phenomena; particular attention will be devoted to the use of formal language and methodological rigor. More specifially, the course aims to complete students preparation in Econometrics by being able to deal with advanced econometric models and methods. Moreover, it will give the student an overview of nonlinear and latent variable modeling for financial data analysis.

Knowledge and understanding skills.
Attendance and active participation in lectures, exercise sessions, tutoring activities, together with the individual study will allow the student to acquire the following knowledge and understanding skills:
- know and use the main mathematical tools necessary to represent complex economic phenomena;
- know the mathematical techniques useful to solve and analyze the proposed models.
- know the statistical techniques useful to test the validity of theoretical economic models on data.

Ability to apply knowledge and understanding.
Through the interaction with the instructors, the tutors, and peers and through the individual study the student acquires the following abilities:
- know how to use quantitative instruments to cope with complex problems related to economic and financial environments;
- know how to choose the most appropriate technique in order to solve the concrete problem under analysis.

Judgment skills, communication skills, learning skills.
Regarding the autonomy of judgment, communication skills and learning abilities, through the personal and group study of the concepts seen in class, the student will be able to:
- formulate rational justifications to the approach used to solve economic and financial problems, understanding their relative strengths and weaknesses;
- know how to formulate and communicate sofisticated quantitative analysis of economic and financial data through the use of mathematical models.

Basic notions of Regression Analysis and Specification of Linear Dynamic Econometric Model

1 Bayesian inference
1.1 Decision Theoretical Foundation of Statistics
1.2 Least square and maximum likelihood inference principles
1.3 Bayesian inference: Prior Distribution, Posterior Distribution, Bayesian Estimator
1.4 Bayesian nonparametric methods
2 Numerical methods for simulation-based inference
2.1 Markov-chain Monte Carlo
2.2 Gibbs Sampling
2.3 Metropolis-Hastings
3 Bayesian Linear Regression.
4 Probit and Logit models. Truncation and censoring. Models for count data.
5 Bayesian SUR and VAR
6 Bayesian Latent Variable Models
7 Nonlinearities in Financial Data
7.1 Conditional Heteroscedasticity: ARCH and GARCH Models, Stochastic Volatility Models
7.2 Switching Regime Models
8 State-space models
8.1 Kalman filter
8.2 Hamilton filter
8.3 Particle filters

Notes and slides.
A reading list will be provided for every topic.

The exam consists in individual and group assignments, and in the preparation and presentation of a final project. The exam is evaluated on a 30-point basis. The solution of the assignements can yield up to 20 points over 30 and the final project can yield up to 10 points out of 30. The exam is considered passed with the achievement of 18 total points over 30.

The assignments are intended to verify the progress in the learning activity and the abilities to go deep autonomously to the heart of the topics of the course. The assignments consist of problems to solve and questions to reply regarding additional reading material properly referenced in the text of assignments.

The final project develops or extends further the topics of the course and includes an original contribution of the student, such as new models, analysis of their properties, or original applications to real data. The project preparation aims at putting into practice the knowledge acquired. The oral presentation of the project aim at verifying the level of knowledge of the topics in the projects and the ability to communicate them in a clear and rigorous way.

scritto e orale

Cycles of seminars, lectures on the various topics, group assignements

English

Questo insegnamento tratta argomenti connessi alla macroarea "Cambiamento climatico e energia" e concorre alla realizzazione dei relativi obiettivi ONU dell'Agenda 2030 per lo Sviluppo Sostenibile