Unit of study_

STAT4025: Time Series

Overview

This unit will study basic concepts and methods of time series analysis applicable in many real world problems in numerous fields, including economics, finance, insurance, physics, ecology, chemistry, computer science and engineering. This unit will investigate the basic methods of modelling and analyzing of time series data (i.e. data containing serially dependence structure). This can be 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 ARMA, ARIMA and SARIMA and their properties. Then the identification, estimation, diagnostic model checking, decision making and forecasting methods based on these models will be developed with applications. The spectral theory of time series, estimation of spectra using periodogram and consistent estimation of spectra using lag-windows will be studied in detail. Further, the methods of analyzing long memory and time series and heteroscedastic time series models including ARCH, GARCH, ACD, SCD and SV models from financial econometrics and the analysis of vector ARIMA models will be developed with applications. By completing this unit, students will develop the essential basis for further studies, such as financial econometrics and financial time series. The skills gained through this unit of study will form a strong foundation to work in a financial industry or in a related research organization.

Unit details and rules

Unit code STAT4025 Mathematics and Statistics Academic Operations 6 STAT3925 STAT2X11 and (MATH1X03 or MATH1907 or MATH1X23 or MATH1933) None None No

Teaching staff

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

Assessment

Type Description Weight Due Length
Final exam (Take-home short release) Final Exam
Written exam
60% Formal exam period 2 hours
Outcomes assessed:
Small test Comp A
4 weekly reports 4% plus a computer based R quiz (CQ1) in week 7 worth 6%
10% Multiple weeks
Due date: 04 Apr 2022 at 17:00
one hour
Outcomes assessed:
Small test Comp B
4 weekly reports 4% plus a computer based R quiz (CQ2) in week 13 worth 6%
10% Multiple weeks
Due date: 23 May 2022 at 17:00
one hour
Outcomes assessed:
online quiz worth 10%
10% Week 07
Due date: 08 Apr 2022 at 12:00
one hour
Outcomes assessed:
online quiz worth 10%
10% Week 13
Due date: 27 May 2022 at 12:00
one hour
Outcomes assessed:
= Type D final exam

Assessment summary

• Quiz 1: This an open book quiz. Students can use a University approved non-programmable calculator or R during this quiz. This will be done online in week 7 during your lecture time on Friday 8 May at 11.00 and submit by 12.00 through turnitin. Worth 10%.
• Comp A: This consists of 2 subcomponents during Weeks 2-7: online submission of 4 weekly reports 4% and a Computer quiz (CQ1) in Week 7, Monday 4 April at 16.00 worth 6%. This CQ1 is an online computer exam/quiz (open book). This must be done in your assigned computer class time on Monday and submit through turnitin by 17.00.
• Quiz 2: This is an open book quiz. Students can use a University approved non-programmmable calculator and R during this quiz. This will be done in week13 during your lecture time on Friday 27 May and submit by 12.00 through turnitin. Worth 10%.
• Comp B: This consists of 2 subcomponents during Weeks 8-13: online submission of 4 weekly reports 4% and a Computer quiz (CQ2) in Week 13, Monday 23 May at 16.00 worth 6%. This CQ2 is an online computer exam/quiz (open book). This must done in your assigned computer class time on Monday and submit through turnin by 17.00.
• Final exam: 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.

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.

The Current Student website  provides information on academic integrity and the resources available to all students. The University expects students and staff to act ethically and honestly and will treat all allegations of academic integrity breaches seriously.

We use similarity detection software to detect potential instances of plagiarism or other forms of academic integrity breach. If such matches indicate evidence of plagiarism or other forms of academic integrity breaches, your teacher is required to report your work for further investigation.

You may only use artificial intelligence and writing assistance tools in assessment tasks if you are permitted to by your unit coordinator, and if you do use them, you must also acknowledge this in your work, either in a footnote or an acknowledgement section.

Studiosity is permitted for postgraduate units unless otherwise indicated by the unit coordinator. The use of this service must be acknowledged in your submission.

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.

Weekly schedule

WK Topic Learning activity Learning outcomes
Week 01 1. Time series data, components of a time series; 2. Filtering to remove trends and seasonal components Lecture (3 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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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.

1. Analysis of Financial Time Series, R.S.Tsay, John Wiley 3rd Edition (2010).
2. 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.

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

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

GQ1 GQ2 GQ3 GQ4 GQ5 GQ6 GQ7 GQ8 GQ9

Responding to student feedback

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

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