This course will be useful to students who plan to take empirically oriented finance courses as well as students who want to get a solid understanding of the tools required to analyze and model financial asset prices and, more generally, economic time series related to any field of economics and management. The link between statistical models and their implementation is emphasized.

The course fits into the overall program curriculum pursuing some of the defined general learning goals. In particular, the course contributes to the development of the following capabilities:

• Identify trends, technologies and key methodologies in a specific domain (specialization streams)

• Design solutions applying a scientific and engineering approach (Analysis, Learning, Reasoning, and Modeling capability deriving from a solid and rigorous multidisciplinary background) to face problems and opportunities in a business and industrial environment

With respect to the first learning goal, at the end of the course students will be able to:

• Understand the key aspects of statistical time series models, and how these models can be used to forecast economic variables and analyze their relationship

• Understand the differences between univariate and multivariate time series models

• Understand the importance of confidence intervals associated to point forecasts
• Understand the notion and relevance of stationarity in time series analysis
• Understand the key aspects of dynamic volatility models

With respect to the second learning goal, at the end of the course students will be able to:

• Select the appropriate time series model to apply in practical economic situations.
• Interpret the output of econometric packages implementing time series models
• Use time series models for forecasting economic and financial time series
• Use time series models to support economic decisions

Overview

The course introduces students to financial econometrics, providing them with appropriate techniques for empirical investigation in finance. The emphasis will be on understanding and applying a set of econometric tools that are widely used by academics and practitioners working in quantitative areas such as risk management, investment management, and financial engineering (although most of the techniques are widely used also in empirical macro and monetary economics). After a quick review of the multiple linear regression model, the course will illustrate univariate and multivariate models for time series analysis and forecasting. The analysis of non-stationary time series will be discussed, illustrating the theoretical and empirical relevance of the notion of integration and cointegration. The course also covers dynamic models for volatility analysis (ARCH and GARCH models) and one topic, possibly varied from year to year (event studies, Markov switching models, Factor models, ...). Providing the students with the ability to use the models is one of the goals: to this aim, problem sets with both analytical and computer-exercise components will be a relevant part of the course.

Main topics

• 0. Refresher on the linear multiple regression model: estimation through Ordinary Least Squares, checking assumptions (functional form, multicollinearity, heteroskedasticity, autocorrelation, non-normality)
• 1. Univariate analysis of time series: Stochastic processes and their properties. AR, MA and ARMA models. Analysis of trend, cycle and seasonality.
• 2. Multivariate analysis of time series: ARX models and VAR models
• 3. Analysis of nonstationary univariate and multivariate time series: integration and cointegration
• 4. Models for the analysis of volatility: ARCH and GARCH models.
• 5. One of the following topics: Event studies, econometric aspects of the CAPM, econometrics  of the efficient frontier, econometrics of derivatives, analysis of ultra-high frequency financial data, long memory processes, Markov switching models, ... The topic will be chosen at the beginning of the course. Students willing to deepen autonomously, for some reason, a different topic instead of the chosen one, may propose it.

The course is self contained. However some prior knowledge of statistical inference (estimation and testing theory) and of the linear regression model is preferable. Taking the course Introductory Econometrics in advance would be perfect, but it is not required.

(i) Written exam (80 minutes, weight 60%). The written exam is based on two exercises (the first is on the topics 1, 2 and 3 illustrated above; the second is on the topics 4 and 5). The main purpose of the written exam is to assess the achievement of the second learning goal and the associated learning objectives (ability to select the appropriate model to answer research questions, to read the output of time series packages, to forecast economic time series based on time series model, to use the models to support economic decisions)

(ii) Oral exam (15 minutes, weight 40%). The main purpose of the oral exam is to assess the achievement of the first learning goal and the associated learning objectives (understanding of the main theoretical aspects of time series models). The oral exam has to be taken after the written exam, not necessarily in the same call.

(iii) Non-compulsory team project work  (2 students): a paper about 10/15 pages long, where some of the techniques illustrated in the course is applied to a real problem; the paper has to be illustrated in a 30 minutes presentation, possibly via skype; the project work may increase the final mark by at most 2/30. The project work gives you the opportunity to get an hands-on perspective on the discipline. Highly recommended if you plan to include some time series analysis in your final thesis, or if you think that a deep understanding of statistics in general and time series analysis in particular is a valuable asset for your future.

Chapters 1 to 8