STATS 7058 - Time Series
North Terrace Campus - Semester 2 - 2015
General Course Information
Course Code STATS 7058 Course Time Series Coordinating Unit Statistics Term Semester 2 Level Postgraduate Coursework Location/s North Terrace Campus Units 3 Contact Up to 3 hours per week Available for Study Abroad and Exchange Y Prerequisites STATS 2107 or (MATHS 1012 and ECON 2504) or (MATHS 2201 and MATHS 2202) Assumed Knowledge Experience with the statistical package R such as would be obtained from STATS 1005 or STATS 2107 Course Description 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.
Course Coordinator: Associate Professor Inge Koch
The full timetable of all activities for this course can be accessed from Course Planner.
Course Learning Outcomes1 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.
University Graduate Attributes
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
Recommended ResourcesRobert 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 LearningThis 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.
Link to MyUni login page:
Learning & Teaching Activities
Learning & Teaching ModesThis 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 SummaryLecture 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
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
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
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
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Component Weighting Outcomes Assessed Assignments 16% All Individual Projects 4% All Test 20% All Exam 60% All
Assessment Related RequirementsAn aggregate score of at least 50% is required to pass the course.
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%
Individual projects throughout the semester: 4%
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Late assignments will not be accepted.
Assignments will have a two week turn-around time for feedback to students.
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M10 (Coursework Mark Scheme) Grade Mark Description 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
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