D1. Knowledge and understanding By the end of the course, the student will be acquainted with the major concepts, models and issues of basic econometrics, with special reference to financial applications. D2. Applying knowledge By the end of the course, the student will be able to apply standard econometric techniques for solving a variety of estimation and forecasting problems. D3. Independence By the end of the course, the student is expected to know which models and techniques best fit different applications and goals, being able to independently perform simple econometric analyses. D4. Verbal skills By the end of the course, the student will expand its vocabulary towards technical words and concept typical of the financial econometric domain, easing further readings on the topic. D5. Learning abilities. The course provides a general introduction on some common techniques and methods of basic econometrics with applications to finance. On this basis, the student will be able to independently deepen its knowledge on the field and understand more advanced papers on the topic.

Elementary probability: random variables, conditional and unconditional expectation, variance, covariance and correlation, convergence, distributions and conditional expectations. Good understanding of the Normal distribution. Elementary statistics: simple linear model (will be reviewed), general understanding on likelihood, least squares and hypothesis testing –related principles. Math: vector and matrix algebra (will be extensively reviewed), derivatives, integrals. Software: basic usage of any software suitable for statistical data analysis.

Scope and purpose of Econometrics. Types of data.

Simple linear regression. Regression vs. correlation. Assumptions of the classical linear model. Properties of the errors.

Derivation of the OLS estimator. Precision and standard errors.

Generalization to multiple regressors: the OLS estimator in matrix form. Multiple hypothesis testing. Goodness of fit. Specification analysis.

Violations of the classical hypotheses and diagnostic testing.

Univariate time series modelling. Stationarity and autocorrelation. Stochastic processes. Specification and estimation of time series models.

Unit root testing. Cointegration. Models in levels and error correction representations.

Models for panel data. Individual heterogeneity and fixed effects estimators.

Brooks, Introductory Econometrics for Finance, IV Ed. (Cambridge),

Ch 1 all but 1.7, 1.8

Ch 2 all but 2.3.6, 2.3.7

Ch 3 all but 3.5, 3.13

Ch 4 all but 4.11, A.4.2

Ch 5 all but 5.13

Ch 6 until 6.4.1

Ch 8: 8.1, 8.4, 8.5, 8.6, 8.7.1

Ch 11 until 11.5

Scope and purpose of Econometrics. Econometrics vs. Financial Econometrics. Types of data (cross-sections vs. time series, panel data).

Simple linear regression. Regression vs. correlation. Assumptions of the classical linear model. Properties of the errors. Derivation of the OLS estimator. Precision and standard errors.

Introduction to statistical inference. Testing in the context of the classical linear model. The t-ratio. Example: the CAPM model; testing hypotheses on beta, Jensen's Alpha.

Generalization to multiple regressors. The OLS estimator in matrix form: derivation of the estimator and of its covariance matrix. Examples: hedonic house pricing and the APT model.

Multiple hypothesis testing: the F-test. Goodness of fit statistics and their relation to the F-test. Specification analysis: encompassing models and tests of non-nested hypotheses. Omitted and redundant regressors.

Violations of the classical hypotheses: diagnostic testing for heteroskedasticity and for correlation; testing for normality and for the wrong functional form. Parameter stability: testing for breakpoints; dummy variables. Example: determinant of sovereign ratings.

Univariate time series modelling. Definition of stationarity. Stochastic processes: white noise, AR, random walk. Autocorrelation and partial autocorrelation functions; specification analysis of univariate models. Dynamic regression models and conditions for their consistency.

Stationarity and unit root testing; DF and ADF tests. Definition of cointegration. Notion of superconsistency. Modelling cointegrating or noncointegrating data: levels and error correction representations vs. the first differenced model.

Models for panel data. Individual, potentially correlated heterogeneity and inconsistency of the pooled OLS estimator. Least squares dummy variables (LSDV) and fixed effects (FE) estimators. Specification analysis.

Traditional face-to-face lessons. Discussion on empirical examples, with possible exercise sessions either in the lab or at home.

Additional materials (slides, papers) will be available on Moodle2.

The assessment of learning is conducted through an oral exam consisting of: - theoretical questions to assess the student's ability to provide detailed answers on specific topics of the program - applied questions (solving exercises or interpreting results of statistical procedures) to verify the student's ability to use the proposed statistical methods and interpret the results. The duration of the exam generally ranges from half an hour to an hour and a half, depending on the need to ascertain the level of knowledge achieved. A preliminary written exam, containing questions of the same nature as those in the oral, can be added in case of very crowded exam sessions. The exam is passed with a minimum score of 18/30 if a sufficient knowledge of the required topics is demonstrated along with an acceptable expository ability.

This course explores topics closely related to one or more goals of the United Nations 2030 Agenda for Sustainable Development (SDGs) (see below, 1, 2, 8, 10, 16).