NMAK14022U Statistics for non-linear time series models (AAM)

Volume 2014/2015
Education
MSc programme in Actuarial Mathematics
MSc Programme in Mathematics
MSc Programme in Statistics
MSc Programme in Mathematics-Economics
Content

Statistics for non-linear time series models

Time series are stochastic processes sampled at discrete instants of time; they are observed in nature, economy and society. Time
series are available in abundance in the form of returns of financial assets (as high and low frequency data) ,as time series related to the Internet such as file sizes, length of transmission duration of files, time series of medical oberservations on patients, etc.

What these time serie have in common is that they are typically of non-linear
structure, i.e. the present observation does not depend in a linear way on the past oberservations. The course aims at providing statistical tools for non-linear time series in particular on volatility models. The GARCH, exponential GARCH, stochastic volatility models belong to this class. They are major models in econometrics and financial time series analysis. We will study parameter
estimation, the selection of models and prediction with application to quantitative risk measures. During the course, the theory will be applied to real-life data in order to show the strength and the limitations of the methods.

Learning Outcome

Knowledge:

At the end of the course the student will be familiar with modern estimation techniques, model selection methods and prediction technology for non-linear time series  models, in particular for financial time series models.

Skills:

The student will be able to fit real-life data to parametric non-linear processes, in particular common financial time series models such as GARCH and stochastic volatility models. He/she will be able to apply standard software (R) to achieve the goals.

Competences:

The student will learn about the advantages and limitations of non-linear
time series models. He/she will be able to read textbooks and monographs on the topic in the fields of econometrice, time series analysis, statistics and actuarial science.

Lecture notes will be provided.

Basic knowledge of probability theory, statistics and stochastic processes
5 hours of lecture per week for 7 weeks.
  • Category
  • Hours
  • Exam
  • 66
  • Lectures
  • 35
  • Theory exercises
  • 105
  • Total
  • 206
Credit
7,5 ECTS
Type of assessment
Continuous assessment
Continuous assessment consisting of a final oral examination (30 minutes without preparation time and without aids) and two take home exams.

The oral examination counts for 70% of the grade. The remaining 30% correspond to a Mid Term (15%) and a Final Term Test (15%). In these take home tests, the student will solve some theoretical problems and get statistical expertise on simulated and real-life data, mostly from insurance and finance applications. The student must receive more than 50% of the marks for each of the Mid Term and the Final Term Tests. Otherwise the grade for the course is -3.
Aid
Without aids

The oral final exam is without aids. All aids are allowed for the two tests.

Marking scale
7-point grading scale
Censorship form
No external censorship
Several internal examiners at the oral exam, one internal examiner at the take home exams.
Re-exam
Oral examination (30 minutes) with internal censor without preparation time and notes. The student is admitted to the re-examination if he/she has received more than 50% of the marks in both the Mid Term and the Final Term Tests. If this has not been achieved at the time of the first examination the student may resubmit the two tests before the re-examination.
Criteria for exam assesment

The student must in a satisfactory way demonstrate that he/she has mastered the learning outcome of the course.