COURSE UNIT TITLE

: NONLINEAR TIME SERIES ANALYSIS

DEGREE PROGRAMMES

Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS
STA 5078 NONLINEAR TIME SERIES ANALYSIS 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

The course provides a introduction of non-linear time series models, such GARCH, Markov-switching as well as threshold autoregressive time series models. Student will study their common probabilistic and statistical concepts and theory (Markov chains with uncountable state space, stochastic recurrence equations, ergodicity and mixing). Finally, derivation of estimators for the model parameters will obtain.

Learning Outcomes of the Course Unit

1   To understand the dynamical system,
2   To get some information about the nonlinear time series models,
3   To determine the probability structure of dynamical system,
4   To identify the dynamical system with statistical aspects and methods,
5   To make nonlinear prediction.

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week Subject Description
1 From linear oscillations to nonlinear oscillitaions, limit cycles, local linearization of nonlinear differential equations
2 Time Delay, chaos of nonlinear difference equations, stability theory of difference equations
3 Nonlinear autoregression, Autoregressive models with discrete state space, threshold models
4 Deterministic stability, stochastic stability, and ergodicity, stationary distributions, time reversibility, invertibility
5 Test for linearity, model selection, graphical methods for initial data analysis, estimation and diagnostics
6 Basic properties of Autoregressive models with conditional heteroscedasticity (ARCH) and generalized ARCH, Preparing Individual Assignments
7 Estimation, Asymptotic Properties of Conditional MLEs
8 Testing for the ARCH Effect, Generalized Likelihood Ratio Tests (GLR), Preparing Individual Assignments
9 Power of GLR, Feature of Nonlinear Prediction
10 Decomposition for Mean Square Predictive Errors, Noise amplification, Preparing Individual Assignments
11 Sensitivity to Initial Values, Nonlinear versus Linear Prediction
12 Point Prediction, Local Linear Predictors, Preparing Individual Assignments
13 Estimating Predictive Distributions
14 Interval Predictors and Predictive Sets

Recomended or Required Reading

Textbook(s): Fan, J. Yao Q., Nonlinear Time Series Nonparametric and Parametric Methods, Springer, 2003.
Supplementary Book(s): Tong H., Non-linear Time Series- A dynamical System Approach, Oxford, 2003.

Planned Learning Activities and Teaching Methods

Lecture, homework assignments, problem solving

Assessment Methods

SORTING NUMBER SHORT CODE LONG CODE FORMULA
1 ASG ASSIGNMENT
2 FIN FINAL EXAM
3 FCG FINAL COURSE GRADE ASG * 0.50 + FIN * 0.50
4 RST RESIT
5 FCGR FINAL COURSE GRADE (RESIT) ASG * 0.50 + RST * 0.50


Further Notes About Assessment Methods

If the instructor needs to add some explanation or further note, this column can be selected from the DEBIS menu.

Assessment Criteria

Evaluation of homework assignments, presentation, project report 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: 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 14 2 28
Preparation for final exam 1 39 39
Preparing assignments 4 22 88
Preparing presentations
Final 1 2 2
TOTAL WORKLOAD (hours) 199

Contribution of Learning Outcomes to Programme Outcomes

PO/LOPO.1PO.2PO.3PO.4PO.5PO.6PO.7PO.8PO.9PO.10
LO.1555
LO.2555
LO.3555
LO.4555
LO.5555

CONTACT INFORMATION
Dokuz Eylül Üniversitesi Cumhuriyet Bulvarı No: 144 35210 Alsancak / İZMİR
Phone: +90(232) 412 12 12 - Fax: +90 (232) 464 81 35

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