Unit STATISTICAL METHODS FOR ECONOMY AND FINANCE
- Course
- Finance and quantitative methods for economics
- Study-unit Code
- A000201
- Location
- PERUGIA
- Curriculum
- Statistics for finance and economics
- Teacher
- Luca Scrucca
- CFU
- 12
- Course Regulation
- Coorte 2020
- Offered
- 2020/21
- Type of study-unit
- Obbligatorio (Required)
- Type of learning activities
- Attività formativa integrata
STATISTICAL LEARNING AND DATA MINING
| Code | A000203 |
|---|---|
| Location | PERUGIA |
| CFU | 6 |
| Teacher | Luca Scrucca |
| Teachers |
|
| Hours |
|
| Learning activities | Caratterizzante |
| Area | Matematico, statistico, informatico |
| Academic discipline | SECS-S/01 |
| Type of study-unit | Obbligatorio (Required) |
| Language of instruction | English |
| Contents | Advanced statistical methods for Data Mining, both supervised (classification and regression) and unsupervised (clustering and dimension reduction). Real data case studies introduced and analysed using the software R. |
| Reference texts | James G., Witten D., Hastie T. and Tibshirani R. (2013) An Introduction to Statistical Learning with Applications in R. Springer-Verlag. Supplemental material will be provided by the instructor during the course. |
| Educational objectives | Upon completion of this course the student should be able to apply independently the appropriate statistical methods to real regression, classification, and clustering problems, through the use of the software R. |
| Prerequisites | A basic knowledge of statistics, both descriptive and inferential, and the linear regression model. |
| Teaching methods | Lectures and practical sessions in the computer lab. |
| Other information | Attending classes is not mandatory but strongly advised. |
| Learning verification modality | Progress assessments and final oral exam. The computer laboratory activities are aimed to assess the student's ability to put into practice the methods introduced in the classroom. Final oral examination instead intends to assess the level of knowledge and understanding achieved by the student regarding the computational and methodological aspects covered during the course. |
| Extended program | The course aims at presenting advanced statistical methods for Data Mining, both supervised (classification and regression) and unsupervised (clustering and dimension reduction). These methods have been successfully applied in many fields, from finance to economy, from business analytics to natural and social sciences. Real data case studies will be introduced and analysed using the statistical software R. Specifically, the following topics will be covered: - Statistical learning and data mining. - Prediction vs interpretation. - Supervised vs unsupervised learning. - Classification vs regression. - Evaluating the accuracy of a statistical model. - Supervised learning: introduction. - Extensions to the linear model: model selection and regularisation. Polynomial regression, splines, generalised additive models. - Resampling methods: cross-validation and bootstrap. - Classification: introduction. - Logistic model and multinomial model. - Linear and quadratic discriminant analysis. - Gaussian naive Bayes. - Gaussian finite mixture models. - k-nearest neighbour algorithm. - Advanced methods for regression and classification: Artificial neural networks, Decision trees, Bagging, Random forests, Boosting. - Unsupervised learning: introduction. - Principal component analysis. - Similarity measures and distance matrix. - Cluster analysis: hierarchical methods. - Non-hierarchical methods: k-means. - Model-based clustering. |
STATISTICAL METHODS FOR FINANCE (MOD.I)
| Code | A000202 |
|---|---|
| Location | PERUGIA |
| CFU | 6 |
| Teacher | Luca Scrucca |
| Teachers |
|
| Hours |
|
| Learning activities | Caratterizzante |
| Area | Matematico, statistico, informatico |
| Academic discipline | SECS-S/01 |
| Type of study-unit | Obbligatorio (Required) |
| Language of instruction | English |
| Contents | Introduction to statistical software R. Statistical inference: method of maximum likelihood estimation. Regression: simple and multiple linear regression model; logistic regression. Analyses and real data case studies. |
| Reference texts | Weisberg, S. (2014) Applied Linear Regression, 4th edition, Wiley Ruppert, D. and Matteson, D.S. (2015) Statistics and Data Analysis for Financial Engineering, 2nd ed., Springer Supplemental material will be provided by the instructor during the course. |
| Educational objectives | Upon completion of this course the student will be able to apply to real data problems the methods of statistical inference, linear and logistic regression, studied through the use of the software R. |
| Prerequisites | Fundamentals of statistics (descriptive statistics and statistical inference). |
| Teaching methods | Lectures and use of statistical software R. |
| Other information | Attending classes is not mandatory but strongly advised. |
| Learning verification modality | The exam consists in a written test with open questions about theoretical topics and interpretation of the output from the R software for data analysis. |
| Extended program | Introduction to the statistical software R. The method of maximum likelihood: likelihood and log-likelihood function, maximum likelihood estimates (MLEs), Score function and Fisher information, statistical properties of MLEs, numerical computation of MLEs, likelihood ratio test and likelihood-based confidence intervals. Fitting distributions to log-returns by maximum likelihood. Regression models: simple and multiple linear regression, parameter estimation, least squares method and maximum likelihood method, hypothesis testing, confidence intervals, categorical predictors, analysis of variance, goodness of fit, transformations, model selection methods, diagnostic and residual analysis, multicollinearity. Logistic regression: model specification, parameter interpretation and estimation. |