Mathematical Methods for Data Analysis in Economics

Course Objectives. This course concerns the description of identification techniques, with particular reference to the family of equation errors models used for prevision and control. At the end of the course the students should achieve the capability of using identification tools in modeling real processes and in evaluating the quality of the obtained models.

Course Program. From Data to Model: Laws and models. Problems of prediction, time series analysis, clustering, control. Model accuracy versus complexity. Data treatment. Basic probability and statistics: density and joint density, second order description, covariance function, estimator and their properties. Central limit theorem and ergodicity. Bayesian estimation: Gaussian case, linear minimum variance estimators. Discrete time dynamical systems for stochastic processes (ARMA, ARMAX, ARX) predictors. Kalman filter. Correlation and spectral analysis. Kolmogorov-Wiener prediction. Simple non-linear models. Yule-Walker equations and Durbin-Levinson algorithm. Applications: Data analysis for the best production and allocation of resources. Estimation of models for financial engineering and models in healthcare management.

Lab activity: Data analysis and model identification are the subjects of many software tools available on the market and are extensively used in the work environment. The purpose of the lab activity is to expose the student to the main tools of this type. Thus any student will be presented some snapshots drawn from experimental data, from them the student’s task will be to estimate the parameters of a sensible model suitable in describing the underlying phenomenon or the systems, and then tackle problems of prediction, classification and control.