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 (ie. 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.

### Details

Academic unit Mathematics and Statistics Academic Operations STAT4025 Time Series Semester 1, 2020 Normal day Camperdown/Darlington, Sydney 6

### Enrolment rules

 Prohibitions ? STAT3925 STAT2X11 and (MATH1X03 or MATH1907 or MATH1X23 or MATH1933) None No

### Teaching staff and contact details

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

## Assessment

Type Description Weight Due Length
Assignment Final take home exam
Take home exam
60% Formal exam period 16 pages
Outcomes assessed:
Tutorial quiz Comp A
4 weekly reports 4% and a Compute quiz (QC) worth 6%
10% Multiple weeks See Canvas
Outcomes assessed:
Tutorial quiz Comp B
4 weekly reports 4% and a Compute based assignment worth 6%
10% Multiple weeks See Canvas
Outcomes assessed:
Tutorial quiz Quiz 1
Completed online
10% Week 07 1 hour
Outcomes assessed:
Assignment Quiz 2
Assignment - online submission
10% Week 12 See Canvas
Outcomes assessed:
• Quiz 1: You are allowed to bring one two-sided A4 sheet of handwritten notes as well as a University approved non-programmable calculator. This will be done online, in week7 during your lecture time on Thursday. Worth 10%.
• Comp A: This consists of 2 subcomponents during Weeks 2-7: online submission of 4 weekly reports 4% and a Compute quiz (QC) worth 6%. The QC is an online computer exam/quiz (Open book). This must be done online, in week 7, in your assigned computer class time on Monday.
• Quiz 2: This will be an assignment worth 10%. Online submission is due in week 12.
• Comp B: This consists of 2 subcomponents during Weeks 8-13: online submission of 4 weekly reports 4% and a Compute based assignment worth 6%. Online submission is due in week13.

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.

### Special consideration

If you experience short-term circumstances beyond your control, such as illness, injury or misadventure or if you have essential commitments which impact your preparation or performance in an assessment, you may be eligible for special consideration or special arrangements.

The Current Student website provides information on academic honesty, academic dishonesty, 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 dishonesty or plagiarism seriously.

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

## 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 (3 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 (3 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 (3 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 (3 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 (3 hr)
Week 07 1. An introduction to spectral theory of time series; 2. Spectral density function (sdf) of an ARMA model; 3. Examples Lecture (3 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 (3 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 (3 hr)
Week 10 1. Generalised fractional processes. Gegenbaur processes; 2. Spectral properties of Gegenbauer processes; 3. Estimation of parameters of Gegenbauer models Lecture (3 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 (3 hr)
Week 12 1. An introduction to VAR and vector ARIMA models; 2. Spectral properties; 3. Estimation Lecture (3 hr)
Week 13 1. State-space models and their properties; 2. Quasi maximum likelihood estimation (QMLE) Lecture (3 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

## Closing the loop

### 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