Course: 2019/2020

Quantitative Methods I

(17162)

Students are expected to have completed

Foundations of Statistics

The aim of the course is to review, at an intermediate level, the basic concepts and methods of Linear Regression. Emphasis is both in theory and applications.

Description of contents: programme

1. INTRODUCTION.
** 1.1 Formulation and meaning of a statistical regression problem.
** 1.2 Regression models. Goals of a regression analysis.
** 1.3 Data in a regression analysis.
** 1.4 Regression software.
2. THE MULTIPLE LINEAR REGRESSION MODEL: ESTIMATION.
** 2.1 Definition and matrix expression.
** 2.2 Least squares estimation.
** 2.3 Analysis of variance.
Appendix:
** A.1 The multivariate normal distribution.
3.THE MULTIPLE LINEAR REGRESSION MODEL: HYPOTHESIS
TESTING AND CONFIDENCE REGIONS.
** 3.1 The F-test for the general linear hypothesis.
** 3.2 Confidence regions.
** 3.3 Prediction intervals.
Appendix:
** A.1 Indicator variables.
4. MULTICOLLINEARITY, RESIDUAL ANALYSIS, AND DIAGNOSTIC
TECHNIQUES.
** 4.1 Multicollinearity: description and consequences.
** 4.2 Residual analysis.
** 4.3 Outliers and extreme cases.
5. GENERALIZED LEAST SQUARES THEORY.
** 5.1 Cases of known and unknown covariance matrix.
** 5.2 Heteroscedasticity.
** 5.3 Transformations.
** 5.4 Serial correlation.
6. TIME SERIES MODELS
** 6.1 Autoregressive (AR) and moving average (MA) models.
** 6.2 ARMA and ARIMA models.

Learning activities and methodology

There will be computer classes, in which the statistical package R will be used with the purpose of illustrating the derivations of the theoretical classes.

Assessment System

- % end-of-term-examination 50
- % of continuous assessment (assigments, laboratory, practicals...) 50

Basic Bibliography

- CHATERJEE, S. and HADI, A. . Regression Analysis by Example, 5th Edn. John Wiley. 2012
- FREES, E.W.. Regression Modeling with Actuarial and Financial Applications. Cambridge University Press. 2010

Additional Bibliography

- KABACOFF, R. L.. R in action: Data analysis and graphics with R, 2nd Edn. . Manning Publications. 2015
- BROCKWELL P. J. and DAVIS, R. A. . Introduction to Time Series and Forecasting, 3rd Edn.. Springer Verlag. 2016
- JAMES, G., WITTEN, D., HASTIE, T. and TIBSHIRANI, R.. An Introduction to Statistical Learning with Applications in R . Springer Verlag. 2013
- KUTNER, M. H., NACHSTEIM, C., and NETER, J.. Applied Linear Statistical Models 4th Edition.. McGraw Hill. 2004
- MATLOFF, N.. The Art of R programming: A Tour of Statistical Software Design. No Starch Press. 2011
- RAWLINGS, J. O., PANTULA, S. G. and DICKEY, D. A.. Applied Regression Analysis: A Research Tool, 2nd Edn.. Springer Verlag. 1998
- WEISBERG, S.. Applied Linear Regression, 4th Edition. Wiley . 2014

**More information: **https://www.uc3m.es/master/business-finance