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
    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
    Prerequisites MATHS 1012
    Assumed Knowledge STATS 2107
    Assessment 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.
    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
  • Learning Resources
    Required Resources
    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.

    Link to MyUni login page:
  • 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%
    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.
    Course Grading

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

    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

    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

    The University places a high priority on approaches to learning and teaching that enhance the student experience. Feedback is sought from students in a variety of ways including on-going engagement with staff, the use of online discussion boards and the use of Student Experience of Learning and Teaching (SELT) surveys as well as GOS surveys and Program reviews.

    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 ( 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.

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