28177 - Statistical Models

Learning outcomes

By the end of the course the student should know the basic theory of normal linear models and models for the analysis of time series. In particular the student should be able:
- to define a statistical model
- to formulate the normal linear model, estimate its parameters and test their significance
- to use the variable selection procedures
- to fit a linear model to a time series
- to estimate trend and seasonality of time series using parametric and non parametric methods
- to analyse time series using appropriate methods

Course contents

The course is divided in two parts, each of 30 hours.
The first part deals with time series analysis. The program consists of the following arguments. Linear models for time series data: linear processes, autoregressive unintegrated moving average processes (ARIMA) , seasonal processes. Identification, estimation and forecasting from ARIMA models. Time series decomposition. Time and frequency domain analysis.
The second part of the course is concerned with the multiple linear regression model: specification (classical and general model), estimation (least squares and maximum likelihood), finite and asymptotic properties of the estimators, hypothesis testing (testing the significance of the single coefficients and of linear constraintss). Selection of predictor variables in the multiple linear regression model. Normal linear models: Analysis of variance. 

Readings/Bibliography

Rencher A. C. (2000). Linear models in Statistics. Wiley.
Brockwell P.J. and Davis R.A. (2002), Introduction to Time Series and Forecasting, Springer

Further readings:

Weisberg S. (2005). Applied Linear Regression. Wiley, third edition.
Brockwell P.J. and Davis R.A. (1991). Time Series: Theory and Methods. Springer

Teaching methods

Lectures, class exercises, laboratory.

Assessment methods

Every week during the course, students receive an homework which consists of theoretical questions, exercises and applications to be done with the computer. Students can decide either to do their weekly homeworks and give them to the teacher or to exercise when they like. In the former case, students have direct access to an oral exam which is a discussion of the homweork themselves (with the aim of verifying if they have really done and understood the exercises). In the latter case, students will be required to give a written examination, which essentially is a synthesis of the homework, i.e. it is made by theoretical questions, exercises or proofs and comments to a code. The written exam will be contextually discussed in an oral exam. The final mark will be assigned based on the level of preparation and consciousness of the student.

Teaching tools

Textbook, notes and papers that can be found on the institutional teacher web-site and in Alm@DL.

Links to further information

http://www2.stat.unibo.it/luati

Office hours

See the website of Alessandra Luati