Time Series

Year
1
Academic year
2019-2020
Code
02002168
Subject Area
Mathematics
Language of Instruction
Portuguese
Mode of Delivery
Face-to-face
Duration
SEMESTRIAL
ECTS Credits
6.0
Type
Compulsory
Level
2nd Cycle Studies - Mestrado

Recommended Prerequisites

Basic knowledge in Probability and Statistics; experience in using software.

Teaching Methods

Classes are expository and include examples and exercises for applying the acquired knowledge. Throughout the semester, students will do a computational assignment. This assignment is geared towards the treatment of temporal real data, of physical or financial nature.

During the semester students may use tutorial time to clarify their difficulties in grasping the theory and in gaining practical knowledge, as well as in the development of the necessary skills for the computational assignment.

Learning Outcomes

The aim of this course is to provide mathematical methodologies for describing, analysing and forecasting time random features. We begin by studying the general class of linear models which describe different types of data. The study of non-linear models, particularly adjusted for volatile data, in particular of financial type, is also another purpose of this course. Thus, we develop the study of conditionally heteroscedastic processes and bilinear models. Fitting this kind of modeling to real data, by using appropriate software, is another goal of this class.

This course allows developing the following skills: ability to calculate; using computational tools; knowledge of mathematical results; ability to generalize and abstract; formulating and solving problems; design and use of mathematical models for real situations. On a personal level, it allows to develop individual initiative, teamwork, research and independent learning.

Work Placement(s)

No

Syllabus

Stochastic processes – definition and Kolmogorov theorem; second order processes; strong and weak stationarity; autocovariance and autocorrelation functions; autocorrelation partial function; spectral density.

Linear time series models – regular and singular processes; Wold decomposition; ARMA models; characterization theorems for ARMA processes; the class of SARIMA models; Box and Jenkins methodology.

Non-linear time series models – conditionally heteroscedastic processes (GARCH and TARCH models); bilinear models.

Statistical analysis of time series – general estimators for the mean, autocovariance and spectral density functions of a second order stationary process; parametric estimation for regression models with ARCH errors (conditional maximum likelihood and two-stage minimum square estimators).

Fitting to data linear models with conditionally heteroscedastic errors - generalized Box and Jenkins methodology.

Head Lecturer(s)

Maria de Nazaré Simões Quadros Mendes Lopes

Assessment Methods

Assessment
Grading during the semester requires taking 2 mid-term exams (75% of the final grade) and doing a computational assignment (done by a team of 3 students and representing 25% of the final grade). Grading by final examination includes taking an exam (75% of the final grade) and doing a computational assignment (25% of the final grade).: 100.0%

Bibliography

E. Gonçalves, N. Mendes-Lopes, Séries Temporais. Modelações Lineares e Não Lineares, segunda edição, Sociedade Portuguesa de Estatística, 2008.

P. Brockwell, R. Davis, Time Series: Theory and Methods, segunda edição, Springer-Verlag, 2006. 

J. Fan, Q. Yao, Nonlinear Time Series - Nonparametric and Parametric Methods, Springer-Verlag, 2003.

Ch. Francq, J.M. Zakoian, GARCH Models, Wiley, 2010.

Ch. Gouriéroux, Modèles ARCH et Applications Financières, Economica, 1992.

Ch. Gouriéroux, A. Monfort, Séries Temporelles et Modèles Dynamiques, Economica, 1990. 

C. Martins, Modelos Bilineares em Séries Temporais. Propriedades Probabilistas e Decisão Estatística, Tese de Doutoramento, Universidade de Coimbra, 2000.