## STATS 7058 - Time Series

### North Terrace Campus - Semester 2 - 2014

Time Series consist of values of a variable recorded in an order over a period of time. Such data arise in just about every area of science and the humanities, including econometrics and finance, engineering, medicine, genetics, sociology, environmental science. What makes time series data special is the presence of dependence between observations in a series, and the fact that usually only one observation is made at any given point in time. This means that standard statistical methods are not appropriate, and special methods for statistical analysis are needed. This course provides an introduction to time series analysis using current methodology and software. Topics covered are: descriptive methods, plots, smoothing, differencing; the autocorrelation function, the correlogram and variogram, the periodogram; estimation and elimination of trend and seasonal components; stationary processes, modelling and forecasting with autoregressive moving average (ARMA) models; spectral analysis, the fast Fourier transform, periodogram averages and other smooth estimates of the spectrum; time-invariant linear filters; non-stationary and seasonal time series models; ARIMA processes, identification, estimation and diagnostic checking, forecasting, including extrapolation of polynomial trends, exponential smoothing, and the Box-Jenkins approach.

• General Course Information
##### Course Details
Course Code STATS 7058 Time Series Statistics Semester 2 Postgraduate Coursework North Terrace Campus 3 Up to 3 hours per week MATHS 1012 STATS 2107 ongoing assessment 30%, exam 70%
##### Course Staff

Course Coordinator: Associate Professor Inge Koch

##### Course Timetable

The full timetable of all activities for this course can be accessed from Course Planner.

• Learning Outcomes
##### Course Learning Outcomes
1 Demonstrate understanding of the concepts of time series and its application finance and other areas.
2 Demonstrate familiarity with a range of examples for the different topics.
3 Understand the underlying concepts in the time series and frequency domain.
4 Apply ideas to real time series data and interpret outcomes of analyses.
5 Demonstrate skills in communicting mathematics orally and in writing.

This course will provide students with an opportunity to develop the Graduate Attribute(s) specified below:

University Graduate Attribute Course Learning Outcome(s)
Knowledge and understanding of the content and techniques of a chosen discipline at advanced levels that are internationally recognised. 1,2,3,4,5
The ability to locate, analyse, evaluate and synthesise information from a wide variety of sources in a planned and timely manner. 2,4,5
An ability to apply effective, creative and innovative solutions, both independently and cooperatively, to current and future problems. 4,5
Skills of a high order in interpersonal understanding, teamwork and communication. 5
A proficiency in the appropriate use of contemporary technologies. 3,4
A commitment to continuous learning and the capacity to maintain intellectual curiosity throughout life. 1,2,3,4,5
A commitment to the highest standards of professional endeavour and the ability to take a leadership role in the community. 4,5
An awareness of ethical, social and cultural issues within a global context and their importance in the exercise of professional skills and responsibilities. 4,5
• Learning Resources
None.
##### Recommended Resources
Robert H. Shumway & David S. Stoffer, Time Series Analysis and Its Applications With R Examples (second edition), Springer (2006).
C. Chatfield, The Analysis of Time Series: Theory and Practice, Chapman and Hall (1975).
P.J. Brockwell and R.A. Davis, Time Series: Theory and Methods, Springer Series in Statistics (1986).
##### Online Learning
This course uses MyUni exclusively for providing electronic resources, such as lecture notes, assignment papers, sample solutions, discussion boards, etc. It is recommended that students make appropriate use of these resources.

• Learning & Teaching Activities
##### Learning & Teaching Modes
This course relies on lectures as the primary delivery mechanism for the material. Tutorials supplement the lectures by providing exercises and example problems to enhance the understanding obtained through lectures. A sequence of written assignments provides assessment opportunities for students to gauge their progress and understanding.

The information below is provided as a guide to assist students in engaging appropriately with the course requirements.

 Activity Quantity Workload hours Lectures 24 72 Tutorials 6 18 Assignments 4 48 Practicals 6 18 Total 156
##### Learning Activities Summary
Lecture Outline

1. Notation, objectives of time series analysis: description, forecasting and understanding the mechanism generating a series
2. The basic notions of trend, serial dependence and stationarity
3. Measures of dependence, stationary time series
4. Estimation
5. Regression, exploratory data analysis and smoothing
6. MA models
7. AR and ARMA models
8. Difference equations
9. Autocorrelation and partial autocorrelation
10. Forecasting and Durbin-Levinson algorithm
11. Estimation of parameters in forecasting
12. Integrated models for nonstationary data
13. Building ARIMA models
14. Multiplicative seasonals ARIMA models
15. Spectral analysis
16. Cyclic behaviour and peridicity
17. Spectral density
18. Periodogram and discrete Fourier transform
19. Parametric spectral estimation
20. Multiple series and cross-spectra
21. Linear filters
22. Lagged regression models, signal extraction and optimal filtering
23. Introduction to ARCH and GARCH modelling

Tutorial Outline

1. Covariance, weak and strong stationary processes
2. Moving average, differencing, and stationarity
3. AR and MA models
4. Stationarity, invertibility and prediction for ARMA models
5. ARMA model and the derivation of spectral density
6. Periodogram and spectral analysis

Practical Outline

1. Practical time series plot in R
2. Trend fitting and smoothing in R
3. AR and MA models, analyse time series data in R
4. Simulation of ARIMA models and model building in R
5. Explore the basic properties and use of the periodogram in R
6. Cumulative periodogram and fitting linear models in R
• Assessment

The University's policy on Assessment for Coursework Programs is based on the following four principles:

1. Assessment must encourage and reinforce learning.
2. Assessment must enable robust and fair judgements about student performance.
3. Assessment practices must be fair and equitable to students and give them the opportunity to demonstrate what they have learned.
4. Assessment must maintain academic standards.

##### Assessment Summary
 Component Weighting Outcomes Assessed Assignments 16% All Individual Projects 4% All Test 20% All Exam 60% All
##### Assessment Related Requirements
An aggregate score of at least 50% is required to pass the course.
##### Assessment Detail
 Assessment Item Distributed Due Date Weighting Assignment 1 week 1 week 3 4% Assignment 2 week 4 week 6 4% Assignment 3 week 7 week 9 4% Assignment 4 week 10 week 12 4%
Test, Week 10: 20%
Individual projects throughout the semester: 4%
##### Submission
All written assignments are to be submitted to the designated hand-in boxes within the School of Mathematical Sciences with a signed cover sheet attached.
Late assignments will not be accepted.
Assignments will have a two week turn-around time for feedback to students.

Grades for your performance in this course will be awarded in accordance with the following scheme:

M10 (Coursework Mark Scheme)
FNS   Fail No Submission
F 1-49 Fail
P 50-64 Pass
C 65-74 Credit
D 75-84 Distinction
HD 85-100 High Distinction
CN   Continuing
NFE   No Formal Examination
RP   Result Pending

Further details of the grades/results can be obtained from Examinations.

Grade Descriptors are available which provide a general guide to the standard of work that is expected at each grade level. More information at Assessment for Coursework Programs.

Final results for this course will be made available through Access Adelaide.

• Student Feedback

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SELTs are an important source of information to inform individual teaching practice, decisions about teaching duties, and course and program curriculum design. They enable the University to assess how effectively its learning environments and teaching practices facilitate student engagement and learning outcomes. Under the current SELT Policy (http://www.adelaide.edu.au/policies/101/) course SELTs are mandated and must be conducted at the conclusion of each term/semester/trimester for every course offering. Feedback on issues raised through course SELT surveys is made available to enrolled students through various resources (e.g. MyUni). In addition aggregated course SELT data is available.

• Student Support
• Policies & Guidelines
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