Academic Year 2023-2024



Luca Grassetti
Unit Credits
Teaching Period
First Period
Course Type
Prerequisites. The course takes place in the first semester of the first year of Economics master degree course.

The course is one of a set of statistics and econometrics courses in the Economics Master Degree. Notwithstanding, none bridging course is provided for the present teaching activity.

Preliminary knowledge consists of basic statistics topics and econometrics. Advanced statistics courses (as for instance Statistics 2 course – Economics Bachelor Degree) can help the students’ learning process.

Teaching Methods. Course slides (that will be released during the semester) cover the entire course programme but they must be integrated with some other didactic materials.

The main topics will follow the textbook outline. Some specific arguments will be developed following specific alternative material (specific notes and books chapters).

The theory lectures will be completed by some exercise lectures (in the laboratory room) developed considering both didactic and real data examples.

The teaching activity will also consider a group work in which the students will be able to test their knowledge.

Verification of Learning. The final examination consists in:

– a compulsory final written exam (with 5 theoretical questions). The exam is 1 hours and half long;

– a short essay on an additional topic that must be presented at the end of the course (compulsory);

– an empirical analysis developed on a realistic dataset (compulsory);

– an oral examination (optional).

The written exam and the two homework contribute to the final mark for 20, 5 and 5 points respectively. In order to be considered in the final mark computation every individual work must be positively evaluated. The written exam aims at testing the theoretical skills while the group works are used to evaluate the capacity to apply the studied concepts. The optional oral exam is an integration of the written exam. A maximum of three points can be assigned to this test. The test can also be negatively evaluated. Honours will be assigned to students of marked excellence.

Final marks are based on the following framework.

30 e lode – Excellent – The student:

– demonstrates complete and thorough content knowledge;

– demonstrates a deep understanding of even the detailed concepts and is able to synthesize and reflect on them;

– demonstrates an excellent ability to apply the concepts, synthesize them, and make connections between different parts of the subject;

– expresses himself/herself in a confident, clear and accurate manner, structuring his or her discourse in a mature manner.

29-30 – Very good – The student:

– demonstrates complete and thorough content knowledge;

– has a deep understanding of even detailed concepts;

– demonstrates an excellent ability to apply concepts;

– expresses himself/herself in a confident, clear, and accurate manner.

26-28 – Good – The student:

– demonstrates appropriate content knowledge;

– demonstrates an appropriate understanding of the subject;

– applies knowledge appropriately;

– explains clearly using appropriate terminology.

22-25 – Fairly good – The student:

– demonstrates adequate content knowledge, with uncertainties about detailed aspects;

– demonstrates an understanding of the fundamental aspects of the subject;

– demonstrates the ability to apply knowledge with some uncertainty;

– explains the content correctly, with some uncertainty.

18-21 – Sufficient – The student:

– demonstrates limited knowledge of the fundamental aspects of the subject;

– evidences an understanding of the fundamental aspects of the subject;

– shows uncertainty in the application of knowledge;

– explains the content in a simple manner with uncertainties.

<18 – Not Sufficient – The student:

– demonstrates fragmentary and superficial knowledge of the core content of the course;

– demonstrates an inadequate understanding of the basic content of the course;

– shows great uncertainty in the application of the contents;

– explains confusedly and poorly.

More Information. The present course is thought to give an advanced view to the econometric analysis of time series.

It is possible to develop the thesis within the course framework. The thesis work can be both theoretical and empirical.

Given the statistical framework, the focus of the final dissertation must be on the statistical methods and the empirical analysis of financial market.

The present course aims at introducing the students to the empirical analysis of financial markets. Consequently, the specific teaching activity can be considered as propaedeutic to the development of specific empirical analyses proposed in the other Master degree course units.

The students’ evaluation does not present differences between attenders and non-attenders. Also, non-attenders must develop the homework.

The course unit aims to raise awareness of the statistical knowledge applied to financial time series analysis. In particular students will be able to develop an empirical analysis of the time series observed in the financial market.

Course specific knowledge

The course supply the students with advanced tools for time series analysis in the financial market framework.

At the end of the course unit the students will be able to:

– distinguish and evaluate the different kinds of time series;

– develop a preliminary analysis on the data;

– recognise the informative contents of a given dataset;

– decide which model is the best for the specific observed data patterns;

– apply the main time series models and consider also some specific extensions (e.g. threshold models);

– use the software R for the time series analysis.

Soft skills

– topics faced during the semester introduce the time series statistical tools that students can use during the degree courses and, also, in the work framework.

– the students will be able to apply the optimal statistical tool given the empirical framework

– the group works aim at developing the communication skills of students using the ability to summarize the information based on statistical summary statistics, graphical tools and advanced statistical models.

– the skills developed during the teaching can be easily applied in other contexts in order to understand the results of the quantitative analyses.

After a brief preface we will focus on four main arguments:

1. Univariate time series analysis:

– ARIMA models

– Seasonal ARIMA models

2. Threshold linear models

– Threshold AutoRegressive (TAR)

– Self-Exciting TAR (SETAR)

– Smooth Transition AR (STAR)

– Logistic STAR (LSTAR)

– Markov-Switching Models (MSW)

3. Conditional Heterochedasticity models



4. Artificial Neural Networks (ANN)

LaTeX text edit software will be introduced during the teaching period.

R.H. Shumway and D.S. Stoffer. “Time Series Analysis and Its Applications (With R Examples)” (available as a free download)

P.H. Franses and D. van Dijk. “Non-linear time series in empirical finance”, Cambridge University Press, Cambridge, UK (2000)