## STATS 3005 - Time Series III

### North Terrace Campus - Semester 2 - 2017

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 3005 Time Series III School of Mathematical Sciences Semester 2 Undergraduate North Terrace Campus 3 Up to 3 hours per week Y STATS 2107 or (MATHS 1012 and ECON 2504) or (MATHS 2201 and 2202) Experience with the statistical package R such as would be obtained from STATS 1005 or STATS 2107 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 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 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)
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)
All
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
All
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
4,5
• technology savvy
• professional and, where relevant, fully accredited
• forward thinking and well informed
• tested and validated by work based experiences
2,4,5
Self-awareness and emotional intelligence
• a capacity for self-reflection and a willingness to engage in self-appraisal
• open to objective and constructive feedback from supervisors and peers
• able to negotiate difficult social situations, defuse conflict and engage positively in purposeful debate
All
• Learning Resources
None.
##### Recommended Resources
The following books are all useful references for time series theory and applications. I will be referring to the book by Peter Diggle quite a lot.

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).
P. Diggle. Time Series: A Biostatistical Introduction, Oxford Science Publications (1990).
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, such as lecture notes, lecture recordings, assignment and tutorial papers, sample solutions, datasets, practical sheets and so on. 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 and computing workshops supplement the lectures by providing exercises and example problems to enhance the understanding obtained through lectures. A sequence of written assignments and a mid-term test provide 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 5 54 Computing Practicals 6 12 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 Parital 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
##### Specific Course Requirements
None.
• 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.

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.

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