Outline

Overview

This unit will study the basic concepts and methods of time series analysis and forecasting which are applicable in many real-world problems in numerous fields including economics, finance, insurance, physics, ecology, chemistry, computer science and engineering. The first part of this unit will study the basic methods of modelling and analysing time series data (ie. data containing serially dependent structure). This is achieved through learning standard time series procedures on identification of components, autocorrelations, partial autocorrelations and their sampling properties. After setting up these basics, students will learn the theory of stationary univariate time series models including AR, MA, ARMA and ARIMA and their properties. Then the identification, estimation, diagnostic checking, decision making, and forecasting methods from these models will be developed with applications. The second part of this unit of study will consider the spectral theory of stationary time series, estimation of spectra using periodogram and consistent estimation of spectra using lag-windows. Further, the methods of analysing long memory time series through ARFIMA and heteroscedastic time series models including ARCH, GARCH and other volatility models from financial econometrics with applications will be studied. Finally, the theory of cross-correlations, the modelling and analysis of vector ARMA (VARMA) and vector ARIMA (VARIMA) will be studied with applications. Throughout this unit of study, a statistical package will be used to demonstrate various simulations, modelling, forecasting and applications. By completing this unit of study, students will develop essential basis for further studies towards a higher degree in statistics, financial econometrics or financial time series. In addition, the skills gain through this unit of study will form a strong foundation to work in any related area in financial industry or in a suitable research organization.

Unit details and rules

Academic unit	Mathematics and Statistics Academic Operations
Credit points	6
Prerequisites ?	STAT2X11 and (MATH1062 or MATH1962 or MATH1972 or MATH1X03 or MATH1907 or MATH1X23 or MATH1933)
Corequisites ?	None
Prohibitions ?	STAT3925
Assumed knowledge ?	None
Available to study abroad and exchange students	No

Teaching staff

Coordinator	Shelton Peiris, shelton.peiris@sydney.edu.au

Assessment

The census date for this unit availability is 1 September 2025

Details
Criteria

Type	Description	Weight	Due	Length	Use of AI
Written exam ?	Final Exam Written exam. Short answer questions and extended answer questions	60%	Formal exam period	2 hours	AI prohibited
Outcomes assessed:
Contribution	active participation of 10 tutorial classes active participation of 10 tutorial classes	2%	Multiple weeks	50 minutes	AI allowed
Outcomes assessed:
Contribution	active participation of 10 workshops active participation of 10 workshops	2%	Multiple weeks	50 minutes	AI allowed
Outcomes assessed:
In-person written or creative task	Quiz 1 In-class quiz	9%	Week 07 Due date: 15 Sep 2025 at 18:00 Closing date: 15 Sep 2025	40 minutes	AI prohibited
Outcomes assessed:
In-class quiz	Comp A In-class R based quiz (Comp A)	9%	Week 07 Due date: 19 Sep 2025 at 13:00 Closing date: 19 Sep 2025	40 minutes	AI allowed
Outcomes assessed:
In-person written or creative task	Quiz 2 In-class quiz	9%	Week 13 Due date: 03 Nov 2025 at 18:00 Closing date: 03 Nov 2025	40 minutes	AI prohibited
Outcomes assessed:
In-class quiz	Comp B In-class R based quiz (Comp B)	9%	Week 13 Due date: 07 Nov 2025 at 13:00 Closing date: 07 Nov 2025	40 minutes	AI allowed
Outcomes assessed:

Assessment summary

Quizzes : There are two closed book quizes (pen and paper). Students can use a University approved non-programmable calculator during this quiz. This will be done during the Monday lectures in weeks 7 and 13.
Comp A and Comp B: These consist of open R based quizes. These will be done during the workshops in in weeks 7 & 13. You must take these quizzes in your timetabled workshop.
Weekly tutorial attendence and active participation of 10 classes, worth 2%.
Weekly workshop attendence and active participation of 10 classes, worth 2%.
Final exam: This is in the Final exam period. If a second replacement exam is required, this exam may be delivered via an alternative assessment method, such as a viva voce (oral exam). The alternative assessment will meet the same learning outcomes as the original exam. The format of the alternative assessment will be determined by the unit coordinator.
Detailed information for each assessment can be found on Canvas.

Assessment criteria

The University awards common result grades, set out in the Coursework Policy 2014 (Schedule 1).

As a general guide, a high distinction indicates work of an exceptional standard, a distinction a very high standard, a credit a good standard, and a pass an acceptable standard.

Result name	Mark range	Description
High distinction	85 - 100	Representing complete or close to complete mastery of the material.
Distinction	75 - 84	Representing excellence, but substantially less than complete mastery.
Credit	65 - 74	Representing a creditable performance that goes beyond routine knowledge and understanding, but less than excellence.
Pass	50 - 64	Representing at least routine knowledge and understanding over a spectrum of topics and important ideas and concepts in the course.
Fail	0 - 49	When you don’t meet the learning outcomes of the unit to a satisfactory standard.

For more information see guide to grades.

Use of generative artificial intelligence (AI)

You can use generative AI tools for open assessments. Restrictions on AI use apply to secure, supervised assessments used to confirm if students have met specific learning outcomes.

Refer to the assessment table above to see if AI is allowed, for assessments in this unit and check Canvas for full instructions on assessment tasks and AI use.

If you use AI, you must always acknowledge it. Misusing AI may lead to a breach of the Academic Integrity Policy.

Visit the Current Students website for more information on AI in assessments, including details on how to acknowledge its use.

Late submission

In accordance with University policy, these penalties apply when written work is submitted after 11:59pm on the due date:

Deduction of 5% of the maximum mark for each calendar day after the due date.
After ten calendar days late, a mark of zero will be awarded.

Academic integrity

The University expects students to act ethically and honestly and will treat all allegations of academic integrity breaches seriously.

Our website provides information on academic integrity and the resources available to all students. This includes advice on how to avoid common breaches of academic integrity. Ensure that you have completed the Academic Honesty Education Module (AHEM) which is mandatory for all commencing coursework students

Penalties for serious breaches can significantly impact your studies and your career after graduation. It is important that you speak with your unit coordinator if you need help with completing assessments.

Visit the Current Students website for more information on AI in assessments, including details on how to acknowledge its use.

Learning support

Simple extensions

If you encounter a problem submitting your work on time, you may be able to apply for an extension of five calendar days through a simple extension.  The application process will be different depending on the type of assessment and extensions cannot be granted for some assessment types like exams.

Special consideration

If exceptional circumstances mean you can’t complete an assessment, you need consideration for a longer period of time, or if you have essential commitments which impact your performance in an assessment, you may be eligible for special consideration or special arrangements.

Special consideration applications will not be affected by a simple extension application.

Using AI responsibly

Co-created with students, AI in Education includes lots of helpful examples of how students use generative AI tools to support their learning. It explains how generative AI works, the different tools available and how to use them responsibly and productively.

Support for students

The Support for Students Policy reflects the University’s commitment to supporting students in their academic journey and making the University safe for students. It is important that you read and understand this policy so that you are familiar with the range of support services available to you and understand how to engage with them.

The University uses email as its primary source of communication with students who need support under the Support for Students Policy. Make sure you check your University email regularly and respond to any communications received from the University.

Learning resources and detailed information about weekly assessment and learning activities can be accessed via Canvas. It is essential that you visit your unit of study Canvas site to ensure you are up to date with all of your tasks.

If you are having difficulties completing your studies, or are feeling unsure about your progress, we are here to help. You can access the support services offered by the University at any time:

Support and Services (including health and wellbeing services, financial support and learning support)
Course planning and administration
Meet with an Academic Adviser

Weekly schedule

WK	Topic	Learning activity
Week 01	1. Time series data, components of a time series; 2. Filtering to remove trends and seasonal components. Tutorial and introduction to R.	Lecture (5 hr)
Week 02	1. Stationarity time series; 2. Autocorrelation function (ACF) and partial autocorrelation function (PACF) and their properties. Sample autocorrelations and partial autocorrelations; 3. White noise process and probability models for stationary time series	Lecture and tutorial (4 hr)
Week 02	1. Identification of stationarity time series; 2. Computation of autocorrelation function (ACF) and Partial autocorrelation function (PACF) for a given set of data and their properties; 3. ACF of a white noise process	Computer laboratory (1 hr)
Week 03	1. Moving average (MA) models and properties; 2. Invertibility of MA models; 3. Autoregressive (AR) models and their properties; 4. Stationarity of AR models	Lecture and tutorial (4 hr)
Week 03	1. Moving Average (MA) models and investigating properties; 2. Estimation	Computer laboratory (1 hr)
Week 04	1. Mixed autoregressive moving average (ARMA) models and their properties; 2. Homogeneous nonstationary time series (HNTS). Simple models for HNTS; 3. Autoregressive integrated moving average (ARIMA) models and related results; 4. Review of theoretical patterns of ACF and PACF for AR, MA and ARMA processes; 5. Identification of possible AR, MA, ARMA and ARIMA models for a set of time series data	Lecture and tutorial (4 hr)
Week 04	1. Identification of Mixed Autoregressive Moving Average (ARMA); 2. Homogeneous nonstationary time series (HNTS); 3. Autoregressive Integrated Moving Average (ARIMA) models; 4. Identification of possible AR, MA, ARMA and ARIMA models for a set of time series data	Computer laboratory (1 hr)
Week 05	1. Estimation and fitting ARIMA models via MM and MLE methods; 2. Hypothesis testing, diagnostic checking and goodness-of-fit tests. AIC for ARIMA models; 3. Introduction to forecating methods for ARIMA models	Lecture and tutorial (4 hr)
Week 05	1. Estimation and fitting ARIMA models via MM and MLE methods; 2. Hypothesis testing, diagnostic checking and goodness-of-fit tests. AIC for ARIMA models	Computer laboratory (1 hr)
Week 06	1. Minimum mean square error (mmse) forecasting and its properties; 2. Derivation of 1-step ahead mmse forecast function. Forecast updates; 3. Forecast errors, related results and applications	Lecture and tutorial (4 hr)
Week 06	1. Computing minimum mean square error (mmse) forecasts and forecast intervals; 2. Forecast updates; 3.Applications	Computer laboratory (1 hr)
Week 07	1. An introduction to spectral theory of time series; 2. Spectral density function (sdf) of an ARMA model; 3. Examples	Lecture and tutorial (4 hr)
Week 07	1. Visualise the spectral density of various time series; 2. Spectral function (sdf) of an ARMA model; 3. Applications.	Computer laboratory (1 hr)
Week 08	1. Estimation of the sdf using the periodogram; 2. Sampling properties of the periodogram; 3. Smoothed periodogram estimators for the sdf	Lecture and tutorial (4 hr)
Week 08	1. Estimation of the sdf using the periodogram; 2. Sampling properties of the periodogram; 3. Smoothed periodogram estimators for the sdf	Computer laboratory (1 hr)
Week 09	1. An introduction to fractional differencing and long memory time series modelling; 2. Estimation of ARFIMA (p,d,q); 3. Applications of ARFIMA	Lecture and tutorial (4 hr)
Week 09	1. Analysis of long memory time series and modelling; 2. Estimation of ARFIMA(p,d,q); 3. Applications of ARFIMA	Computer laboratory (1 hr)
Week 10	1. Generalised fractional processes. Gegenbaur processes; 2. Spectral properties of Gegenbauer processes; 3. Estimation of parameters of Gegenbauer models	Lecture and tutorial (4 hr)
Week 10	1. Generalised fractional processes. Gegenbaur processes; 2. Spectral properties of Gegenbauer processes; 3. Estimation of parameters of Gegenbauer models	Computer laboratory (1 hr)
Week 11	1. Topics from financial time series/econometrics: conditional heteroscedasticity; 2. ARCH, GARCH processes for heavy tailed data and their properties; 3. Stochastic volatility models and their properties	Lecture and tutorial (4 hr)
Week 11	1. Heavy tailed data and their properties; Analysis of ARCH, GARCH models	Computer laboratory (1 hr)
Week 12	1. An introduction to VAR and vector ARIMA models; 2. Spectral properties; 3. Estimation	Lecture and tutorial (4 hr)
Week 12	Analysis of VAR and VARIMA models. Spectral properties. Estimation.	Computer laboratory (1 hr)
Week 13	1. State-space models and their properties; 2. Applications	Lecture and tutorial (4 hr)
Week 13	Applications; Revision	Computer laboratory (1 hr)

Attendance and class requirements

Due to the exceptional circumstances caused by the COVID-19 pandemic, attendance requirements for this unit of study have been amended. Where online tutorials/workshops/virtual laboratories have been scheduled, students should make every effort to attend and participate at the scheduled time. Penalties will not be applied if technical issues, etc. prevent attendance at a specific online class. In that case, students should discuss the problem with the coordinator, and attend another session, if available.

Study commitment

Typically, there is a minimum expectation of 1.5-2 hours of student effort per week per credit point for units of study offered over a full semester. For a 6 credit point unit, this equates to roughly 120-150 hours of student effort in total.

Required readings

Analysis of Financial Time Series, R.S.Tsay, John Wiley 3rd Edition (2010).
The Analysis of Time Series: An Introduction with R, Chris Chatfield, Haipeng Xing, Chapman and Hall/CRC, 7th Edition (2019).

Learning outcomes

Learning outcomes are what students know, understand and are able to do on completion of a unit of study. They are aligned with the University's graduate qualities and are assessed as part of the curriculum.

Outcomes
Graduate qualities

At the completion of this unit, you should be able to:

LO1. 1. Explain and examine time series data and Identify components of a time series; remove trends, seasonal and other components.
LO2. Identify stationarity time series; sample autocorrelations and partial autocorrelations, probability models for stationary time series.
LO3. Explain homogeneous nonstationary time series, simple and integrated models and related results.
LO4. Apply estimation and ﬁtting methods for ARIMA models via MM and MLE methods. Apply hypothesis testing, diagnostic checking and goodness-of-ﬁt tests
LO5. Apply hypothesis testing, diagnostic checking and goodness-of-fit tests methodology.
LO6. Construct forecasting methods for ARIMA models.
LO7. Explain spectral methods in time series analysis
LO8. Apply financial time series and related models to straightforward problems.
LO9. Apply the methods of analysis of GARCH and other models for volatility.
LO10. Explain and apply methods of vector time series models

Graduate qualities

The graduate qualities are the qualities and skills that all University of Sydney graduates must demonstrate on successful completion of an award course. As a future Sydney graduate, the set of qualities have been designed to equip you for the contemporary world.

GQ1	Depth of disciplinary expertise Deep disciplinary expertise is the ability to integrate and rigorously apply knowledge, understanding and skills of a recognised discipline defined by scholarly activity, as well as familiarity with evolving practice of the discipline.
GQ2	Critical thinking and problem solving Critical thinking and problem solving are the questioning of ideas, evidence and assumptions in order to propose and evaluate hypotheses or alternative arguments before formulating a conclusion or a solution to an identified problem.
GQ3	Oral and written communication Effective communication, in both oral and written form, is the clear exchange of meaning in a manner that is appropriate to audience and context.
GQ4	Information and digital literacy Information and digital literacy is the ability to locate, interpret, evaluate, manage, adapt, integrate, create and convey information using appropriate resources, tools and strategies.
GQ5	Inventiveness Generating novel ideas and solutions.
GQ6	Cultural competence Cultural Competence is the ability to actively, ethically, respectfully, and successfully engage across and between cultures. In the Australian context, this includes and celebrates Aboriginal and Torres Strait Islander cultures, knowledge systems, and a mature understanding of contemporary issues.
GQ7	Interdisciplinary effectiveness Interdisciplinary effectiveness is the integration and synthesis of multiple viewpoints and practices, working effectively across disciplinary boundaries.
GQ8	Integrated professional, ethical, and personal identity An integrated professional, ethical and personal identity is understanding the interaction between one’s personal and professional selves in an ethical context.
GQ9	Influence Engaging others in a process, idea or vision.

Outcome map

Learning outcomes	Graduate qualities
Learning outcomes

Responding to student feedback

This section outlines changes made to this unit following staff and student reviews.

Added new reference books

Additional information

Work, health and safety

We are governed by the Work Health and Safety Act 2011, Work Health and Safety Regulation 2011 and Codes of Practice. Penalties for non-compliance have increased. Everyone has a responsibility for health and safety at work. The University’s Work Health and Safety policy explains the responsibilities and expectations of workers and others, and the procedures for managing WHS risks associated with University activities.

General laboratory safety rules

No eating or drinking is allowed in any laboratory under any circumstances
A laboratory coat and closed-toe shoes are mandatory
Follow safety instructions in your manual and posted in laboratories
In case of fire, follow instructions posted outside the laboratory door
First aid kits, eye wash and fire extinguishers are located in or immediately outside each laboratory

As a precautionary measure, it is recommended that you have a current tetanus immunisation. This can be obtained from University Health Service: unihealth.usyd.edu.au/

Disclaimer

The University reserves the right to amend units of study or no longer offer certain units, including where there are low enrolment numbers.

To help you understand common terms that we use at the University, we offer an online glossary.

Current students

Overview

Overview

Unit details and rules

Teaching staff

Assessment

Assessment

Assessment summary

Assessment criteria

Use of generative artificial intelligence (AI)

Late submission

Academic integrity

Learning support

Learning support

Simple extensions

Special consideration

Using AI responsibly

Support for students

Weekly schedule

Weekly schedule

Attendance and class requirements

Study commitment

Required readings

Learning outcomes

Learning outcomes

Graduate qualities

Outcome map

Responding to student feedback

Responding to student feedback

Additional information

Additional information

Work, health and safety

Disclaimer

On this page

Useful links

STAT4025: Time Series

Semester 2, 2025 [Normal day] - Camperdown/Darlington, Sydney

Overview

Overview

Unit details and rules

Teaching staff

Assessment

Assessment

Assessment summary

Assessment criteria

Use of generative artificial intelligence (AI)

Late submission

Academic integrity

Learning support

Learning support

Simple extensions

Special consideration

Using AI responsibly

Support for students

Weekly schedule

Weekly schedule

Attendance and class requirements

Study commitment

Required readings

Learning outcomes

Learning outcomes

Graduate qualities

Outcome map

Responding to student feedback

Responding to student feedback

Additional information

Additional information

Work, health and safety

Disclaimer

On this page

Useful links