This course aims to provide students with an understanding of various statistical tools commonly used in the analysis of economic and financial data, with a focus on the issue of financial risk. KNOWLEDGE AND UNDERSTANDING. The course will provide the students with the following skills of knowledge and understanding: discuss the main features of financial data and recognize the stylized facts of returns; understand the basics of stochastic processes and the use of some time series models for modeling and forecasting economic and financial time series; consider different approaches to the study of asset volatility and various volatility models. APPLYING KNOWLEDGE AND UNDERSTANDING. At the end of the course, students will be able to exploit the statistical techniques presented in the course for analyzing real data, e.g., performing exploratory data analysis, model selection, and model checking, with the support of the statistical software R. MAKING JUDGEMENTS. At the end of the course, students will have to demonstrate their ability to apply the acquired knowledge and concepts to analyze concrete examples. In particular, students will be asked to interpret, comment, and compare the results from different analyses, making judgments on the appropriateness of the adopted methods. COMMUNICATION SKILLS. By the end of the course, students will be able to articulate their own opinions and questions clearly and participate in a stimulating discussion about the topics covered by the course. LEARNING SKILLS. At the end of the course, students will be able to deepen the topics of the course autonomously and propose appropriate statistical methods for data analysis in the economic and financial fields.

The Statistics course is a prerequisite for this course.

1. Financial markets, prices, and risk: Returns; log returns; multi-period returns; issues for portfolios (Optional: Index numbers and stock market indices) 2. Financial Data and their properties: distributional properties of returns; review of statistical distributions and their moments; visualization of financial data. 3. Linear models for financial time series: characteristics of time series data; stationarity; correlation and autocorrelation function; white noise and linear models; autoregressive models; moving average models; ARMA Models; residual analysis, diagnostics, and model selection; unit-root nonstationarity; integrated ARMA (or ARIMA) models. (Optional: introduction to seasonal models). 4. Forecasting: point forecasts and prediction intervals, exponential smoothing, forecasting using ARMA models. 5. GARCH and conditional volatility: testing for ARCH effects; the ARCH model; GARCH models; fitting ARMA+GARCH Models to financial returns.

J. Danielsson (2011) Financial Risk Forecasting, Wiley Finance R.S. Tsay (2013) An introduction to the analysis of financial data with R, Wiley and Sons D. Ruppert, D.S. Matteson (2015), Statistics and Data Analysis for Financial Engineering, 2nd edition, Springer (supplementary reading) Additional material (slides, exercises, recordings) will be available via the Moodle page of the course.

The course is held using frontal lectures. Practical sessions will be devoted to exercises and R labs in order to explore the basics of R programming for the analysis of economic and financial data. Students will actively participate to the R labs using their own laptop with the software installed. During the course, exercises and quizzes covering the theory and practice will be made available to students for self-evaluation. Students will be strongly encouraged to ask questions and offer comments pertaining to the course.

Any changes to the procedures described above, which are necessary to ensure the application of COVID-19 safety protocols, will be communicated on the DEAMS website and via the Moodle page of the course.

The final exam consists of a written test with open questions and exercises aimed at assessing the student's knowledge of the course topics. The exam also aims at verifying the student's capacity to interpret the output from some statistical analysis performed on real or simulated data with the statistical software R. The duration of the written exams is two hours at the most. The grades are on a scale of 30. A student must receive a minimum score of 18/30 to pass the exam. Questions may have a different weight on the final evaluation, depending on their level of difficulty. The contribution of each exercise to the overall result will be declared in the exam. To pass the exam (18/30) the student must demonstrate that he has acquired sufficient knowledge of the course topics to obtain at least 18 points out of 30. To obtain the maximum score (30/30 cum laude), the student must demonstrate that he/she has acquired an excellent knowledge of all the topics covered during the course and that he/she has participated in the classroom activities and the assignments given during the course. Online registration is mandatory by the indicated deadline.

This course explores topics closely related to one or more goals of the United Nations 2030 Agenda for Sustainable Development (SDGs)