COURSE UNIT TITLE

: ASYMPTOTIC THEORY FOR TIME SERIES

DEGREE PROGRAMMES

Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS
STA 6013 ASYMPTOTIC THEORY FOR TIME SERIES ELECTIVE 3 0 0 8

Offered By

Graduate School of Natural and Applied Sciences

Level of Course Unit

Second Cycle Programmes (Master's Degree)

Course Coordinator

PROFESSOR DOCTOR ESIN FIRUZAN

Offered to

Statistics (English)
STATISTICS (ENGLISH)
Statistics (English)

Course Objective

Modern time series involves a variety of stochastic processes. The stochastic processes are not restricted to the usual AR, MA and ARMA processes. Non-Gaussian linear processes, long-memory processes, nonlinear processes, non-ergodic processes and diffusion processes will be discussed in detail. Much statistical thought relates to issues of estimation and hypothesis testing in the absence of a usable finite sample theory. Statisticians have given to enormous effort for developing adequate asymptotic theory for statistical inference. There is often a link between the introduction of a new model and the development of an asymptotic theory. In consequence, applied statisticians have to estimate time series models for which no asymptotic theory is available. The essential aim of this course is to provide modern asymptotic theory for estimation and testing of hypothesis of time series models.

Learning Outcomes of the Course Unit

1   To understand the stochastic processes,
2   To get some information about the linear process,
3   To get some information about the nonlinear process
4   To determine the probability structure of stochastic processes,
5   To provide information about modern asymptotic theory estimation and testing hypothesis of time series.

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week Subject Description
1 Elements of Stochastic Processes
2 Local Asymptotic Normality for Stochastic Processes
3 Asymptotic Theory of Estimation and Testing for Linear Processes
4 Asymptotic Theory for Nonlinear Stochastic Models
5 Asymptotic Theory for Continuous Time Processes (Stochastic Integrals and Diffusion Processes, Asymptotic Theory for Diffusion Processes)
6 Asymptotic Theory for Continuous Time Processes (Diffusion Processes and Autoregressions with Roots Near Unity, Continuous Time ARMA Processes, Asymptotic Theory for Point Processes), Homework 1
7 Higher Order Asymptotic Theory for Stochastic Processes (Introduction to Higher Order Asymptotic Theory, Valid Asymptotic Expansions)
8 Higher Order Asymptotic Theory for Stochastic Processes (Higher Order Asymptotic Estimation Theory for Discrete Time Processes)
9 Higher Order Asymptotic Theory for Continuous Time Processes (Higher Order Asymptotic Theory for Normalizing Transformations, Higher Order Asymptotics of Iterative Methods), Homework 2
10 Asymptotic Theory for Long-Memory Processes
11 Estimation and Hypothesis Testing Theory for Long-Memory Processes
12 Large Deviation Theory for Stochastic Processes
13 Saddlepoint Approximations for Stochastic Processes, Homework 3
14 Homework Evaluation

Recomended or Required Reading

Textbook(s): Taniguchi, M., Asymptotic Theory of Statistical Inference for Time Series, Springer, 2000.
Supplementary Book(s): White, H. (2002) Asymptotic Theory for Econometricians. (Revised Edition) San Diego: Academic Press.
Van de Vaart (1998). Asymptotic Statistics. Cambridge University

Planned Learning Activities and Teaching Methods

Lecture, homework assignments, problem solving

Assessment Methods

SORTING NUMBER SHORT CODE LONG CODE FORMULA
1 ASG 1 ASSIGNMENT 1
2 ASG 2 ASSIGNMENT 2
3 ASG 3 ASSIGNMENT 3
4 FIN FINAL EXAM
5 FCG FINAL COURSE GRADE ASG 1 + ASG 2 + ASG 3/3 * 0.40 + FIN * 0.60
6 RST RESIT
7 FCGR FINAL COURSE GRADE (RESIT) ASG 1 + ASG 2 + ASG 3/3 * 0.40 + RST * 0.60


Further Notes About Assessment Methods

None

Assessment Criteria

Evaluation of homework assignments and final exam

Language of Instruction

English

Course Policies and Rules

Attendance to at least 70% for the lectures is an essential requirement of this course and is the responsibility of the student. It is necessary that attendance to the lecture and homework delivery must be on time. Any unethical behavior that occurs either in presentations or in exams will be dealt with as outlined in school policy. You can find the undergraduate policy at http://web.deu.edu.tr/fen

Contact Details for the Lecturer(s)

DEU Fen Fakültesi Istatistik Bölümü
e-posta: esin.firuzan@deu.edu.tr
Tel: 0232 301 85 57

Office Hours

To be announced.

Work Placement(s)

None

Workload Calculation

Activities Number Time (hours) Total Work Load (hours)
Lectures 14 3 42
Preparations before/after weekly lectures 13 3 39
Preparation for final exam 1 36 36
Preparing assignments 3 25 75
Final 1 2 2
TOTAL WORKLOAD (hours) 194

Contribution of Learning Outcomes to Programme Outcomes

PO/LOPO.1PO.2PO.3PO.4PO.5PO.6PO.7PO.8PO.9PO.10
LO.1555555
LO.255555
LO.355555
LO.455555
LO.5555555

CONTACT INFORMATION
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Phone: +90(232) 412 12 12 - Fax: +90 (232) 464 81 35

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