## STATS 7058 - Time Series

### North Terrace Campus - Semester 2 - 2018

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 Mathematical Sciences Semester 2 Postgraduate Coursework North Terrace Campus 3 Up to 3 hours per week Y STATS 2107 or (MATHS 1012 and ECON 2504) or (MATHS 2201 and MATHS 2202) Experience with the statistical package R such as would be obtained from STATS 1005 or STATS 2107 ongoing assessment 30%, exam 70%
##### Course Staff

Course Coordinator: Professor Patricia Solomon

##### Course Timetable

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

• Learning Outcomes
##### Course Learning Outcomes
1. Demonstrate advanced understanding of the concepts of time series and their application to health, climate, finance and other areas.
2. Demonstrate familiarity with a range of examples for the different topics covered in the course.
3. Demonstrate an advanced understanding the underlying concepts in the time series and frequency domains.
4. Apply ideas to real time series data and interpret outcomes of analyses.
5. Demonstrate graduade-level skills in communicating mathematics and statistics, 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)
Deep discipline knowledge
• informed and infused by cutting edge research, scaffolded throughout their program of studies
• acquired from personal interaction with research active educators, from year 1
• accredited or validated against national or international standards (for relevant programs)
1,2,3,4
Critical thinking and problem solving
• steeped in research methods and rigor
• based on empirical evidence and the scientific approach to knowledge development
• demonstrated through appropriate and relevant assessment
1,2,3,4
Teamwork and communication skills
• developed from, with, and via the SGDE
• honed through assessment and practice throughout the program of studies
• encouraged and valued in all aspects of learning
5
• Learning Resources
None.
##### Recommended Resources
The following books are useful references for the theory and applications of time series. I will refer to the book by Peter Diggle quite a lot.

P. Diggle. Time Series: A Biostatistical Introduction, Oxford Science Publications (1990).
C. Chatfield. The Analysis of Time Series, 7th Edition, CRC Press (2016).
P.J. Brockwell and R.A. Davis. Time Series: Theory and Methods, 2nd Edition, Springer Series in Statistics (1991).
Robert H. Shumway & David S. Stoffer. Time Series Analysis and Its Applications With R Examples, 3rd Edition, Springer (2016).
##### Online Learning
This course uses MyUni-Canvas for providing electronic resources, including the lecture notes, lecture recordings, assignment and tutorial materials, outlines solutions, datasets, practical sheets and so on. It is recommended that students make appropriate use of these resources. Please ensure you check MyUni regularly for any announcements, emails and discussions.
• Learning & Teaching Activities
##### Learning & Teaching Modes
This course relies on lectures as the primary delivery mechanism for the material. Tutorials and practical classes supplement the lectures by providing exercises and problems to enhance the understanding obtained through lectures. A sequence of written assignments provides assessment opportunities for students to gauge their progress and understanding, and develop their analytical skills using R.

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 5 54 Practicals 6 12 Total 156
##### Learning Activities Summary
Lecture Outline

1. Examples, objectives of analysis, notation, stationarity
2. Smoothing, linear filters, moving average smoothers. serial correlation
3. Iterated smoothing, spline smoothing, autocorrelation and trend. Removing seasonality, decomposing a series, differencing
4. The autocoviance and autocorrletions functions
5. The sample autocorrelation function
6. Statistical properties of the sample autocovariance function. Mean ergodicity. Gaussian white noise
7. Tests for serial correlation. The variogram for unequally spaced data
8. Periodicity and the periodogram
9. The cumulative periodogram
10. Stationary random processes. The general linear process
11. The backward shift operator. The moving average model
12. The autoregressive process. Causality. The Yule-Walker equations
13. ARMA processes
14. Spectral analysis and the spectrum. Wold's Theorem
15. Spectral analysis, aliasing. Convergence of the spectra
16. Spectra for ARMA processes. Processes with continuous spectra
17. ARIMA models. Identification
18. The partial autocorrelation function
19. Identification of ARIMA models. The Akaike Informatio Criterion
20. Likelihood ratio tests. SARIMA models
21. Forecasting for ARMA processes
22. Minimum mean squared error prediction
23. Forecasting with SARIMA models, diagnostics and prediction.

Tutorial Outline

1. Covariances for linear combinations of random variables, the autocovariance function
2. The periodogram
3. Autoregressive and moving average processes
4. The spectrum
5. Multivariate normal distributions and AR(1)
6. Forecasting.

Practical Outline

1. Creating, plotting and smoothing time series in R
2. Smoothing using polynomials, removing trend, and the acf
3. The periodogram
4. Interpreting the periodogram and cumulative periodogram; simulating AR, MA and ARMA processes
5. Simulating ARIMA processes, recognising stationarity and non-stationarity
6. Identifying ARIMA models, estimation, diagnostics and forecasting.
##### Specific Course Requirements
Students taking Time Series as part of a Masters degree will complete additional work, in particular, more advanced assignment, project and practical work for assessment.
• 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 20% All Tutorial and practical participation 10% All Exam 70% 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 3 week 5 4% Assignment 3 week 5 week 7 4% Assignment 4 week 7 week 9 4% Assignment 5 week 9 week 12 4% Tutorials Even weeks 5% Computing Practicals Odd weeks 5% Final exam 70%
5% for Tutorials is awarded for attendance and participation in 5 out of 6 Tutorials.
5% for Computing Practicals is awarded for attendance and participation in 5 out of 6 Practicals.
##### Submission
All written assignments are to be submitted to the designated hand-in boxes on Level 6 of the School of Mathematical Sciences with a signed cover sheet attached.

Late assignments will not be accepted, unless accompanied by a medical certificate or arranged in advance with the Lecturer.

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.

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