Ateneo - UPO

The course aims to introduce students to statistical methods for financial data analysis and simulation techniques in the financial field, with the aid of dedicated software.

Lecture materials provided by the professor, which will be published on the course page on DiR.

References:
- R. Carmona (2014). Statistical Analysis of Financial Data in R. Springer.
- S.T.Rachev, M. Hochestotter, F.J.Fabozzi, S.M. Focardi (2010) Probability and Statistics for Finance. Wiley.

The objective of the course is to provide knowledge and understanding of statistical inference methods and key forecasting techniques. Furthermore, the course aims to equip students with the ability to apply these techniques to the financial sector, developing independent judgment in selecting the appropriate technique, and the ability to present results using correct terminology. The course consists of delivery-based teaching (DE) (approx. 7 ECTS), and interactive teaching (DI) (approx. 1 ECTS).

Linear algebra, calculus, elements of probability and statistics.

Lectures, practical exercises, and computer laboratory activities.

Students with physical disabilities, Learning Disabilities or Special Education Needs can request specific services and tools via the Staff Sviluppo e Coordinamento Carriere e Servizi alle Studentesse e agli Studenti, consulting the University webpage: https://www.uniupo.it/en/services/servicesstudents-physical-or-learning-disabilities Students with disabilities, learning disabilities or special education needs, once they have contacted the University Staff, can refer to the tutor in charge of the course to define the examination modalities, concerning academic aspects.

A mandatory written exam and an optional oral exam (available after achieving a solid passing grade on the written portion, or at the instructor's discretion).

The written exam includes:

-Theoretical questions to assess knowledge of core concepts and mastery of formal language;

Numerical exercises to test practical skills in applying computational algorithms;

Structured problems based on data interpretation and critical commentary on results, designed to evaluate independence in statistical analysis.

The oral exam evaluates:

Acquired theoretical knowledge;

Mastery of technical terminology;

The ability to present and discuss results obtained from real-world data.

Note: After the third attempt at taking the exam within a single calendar year, registration will be automatically blocked.

In addition to the official exam sessions, a midterm exam ("prova parziale") is scheduled, with detailed guidelines published on the course's DIR platform.

Grading Scale and Descriptors:

Below 18 (Fail / Insufficient)
Severely deficient knowledge of theoretical principles of inference; inability to apply models or utilize dedicated software; lack of critical independence and mastery of technical language; confusing, improper, or completely inadequate presentation.

18–24 (Satisfactory / Fair)
Basic but superficial knowledge of inference theory and predictive modeling, with gaps in specific topics; guided application to real datasets via software, with limited ability to interpret results or understand their validity and limits; basic yet correct presentation.

25–28 (Good / Very Good)
Solid knowledge of theoretical principles regarding inferential methods and predictive techniques; independence in applying models to real datasets using software effectively while understanding their limitations; critical thinking; rigor and appropriate technical language.

29–30 cum Laude (Excellent)
Complete, fluid, and deep mastery of the entire subject matter; technical expertise and critical acumen; independence and originality in applying models to real datasets using software effectively while understanding their limitations; rigor and appropriate technical language, demonstrating a comprehensive understanding of the field.

1. Elements of probability. Stochastic independence. Random variables and distributions: mass and density functions. Generating functions. Bivariate probability densities. Random Vectors. Gaussian random vectors and their properties.
2. Statistical Inference. Plug-in approach and Empirical estimates. Maximum likelihood method. Confidence interval. Parametric and nonparametric bootstrap approaches.
3. Testing hypothesis. Errors of I and II type. Critical region. Power of a test. P-value. Parametric tests. Goodness-of-fit tests and normality test (Kolmogorov-Smirmov, Jarque-Bera).
4. Multiple linear regression. OLS principle and maximum likelihhod estimate in the Gaussian case. Test on coefficients and test F.
5. Intoduction to stochastic processes. Weak stationarity. Brownian motion. Simulation of a random process.

By the end of the course, students will be able to:Demonstrate an understanding of the theoretical principles of statistical inference methods and key forecasting techniques for financial data and time series.Apply statistical methods and predictive models to real-world financial datasets using dedicated software.Independently and critically select the most appropriate statistical technique or forecasting model based on the financial phenomenon under study, evaluating its validity and limitations.Clearly and rigorously present the results of quantitative analyses, utilizing correct technical language and appropriate statistical terminology.Develop the methodological skills required to independently pursue further studies.