Te Tari Pāngarau me te Tatauranga
Department of Mathematics & Statistics

STAT352 Applied Time Series

Second Semester
18 points
Not available after 2018

An introduction to the practical aspects of the statistical analysis of time series and its application to the physical sciences and econometrics. Topics include seasonal decomposition, identification and estimation of ARIMA models, seasonal ARIMA models, and forecasting. Time series analysis is the statistical analysis of ordered sequences of data. The distinguishing feature is that these data are correlated. Such data arise in a bewildering range of application areas that include:

  • Climatology: Estimation long term changes of climate
  • Economics: Analysis of quarterly or monthly CPI, unemployment rates
  • Finance: Estimating volatility of stock market returns
  • Dendrochronology: Paleoclimate reconstruction based on series of tree ring widths
  • Sonar: Detection of underwater signals

as well as communications, speech compression, seismology, control theory, and many more.

Paper details

This paper examines a range of statistical techniques that can be used for the analysis of data that has been observed sequentially through time. Topics include seasonal adjustment, identification and estimation of ARMA and ARIMA models, intervention analysis and forecasting. Applications will be drawn from many disciplines ranging from econometrics to environ-mental monitoring.

Potential students

Suitable for students doing a Major or a Minor in Statistics.

It is also of interest to students in Economics or Finance.

Main topics

  • Classical decomposition of time series into a trend, seasonal and irregular component
  • Models for stationary time series; autoregression, moving average and ARMA models; identification, estimation and diagnostic testing; forecasting from ARMA models
  • ARIMA and seasonal ARIMA models for series with trend and seasonal components; forecasting


A course of regression methods such as STAT 241 Regression and Modelling 1 will be sufficient. ECON 210 or FINC 203 are also acceptable. There is no mathematics prerequisite.

Required text

Lecture notes will be available online.

Useful references

P.J. Brockwell and R.A. Davis (2016) Introduction to Time Series and Forecasting (3rd Edition) Springer. Available online in Library

C. Chatfield, (1996) Analysis of Time Series: An Introduction (5th Edition) Chapman and Hall.

P.J. Diggle (1990) Time series: A biostatistical introduction Oxford Science Publications.


Dr Ting Wang, Room 518


Monday and Wednesday, 1pm, room MA240, Science III building.

Thursday, 12noon, room MA240, Science III building. Thursday lectures will be on odd-numbered semester weeks only, starting in the first week: 1, 3, 5, 7, etc.

(Subject to change with notice in advance)


Thursdays 3pm, MA124 (level 1 computing lab, Science III), starting in week 2 of semester.

Internal Assessment

The internal assessment is made up from 5 assignments and 1 mid-semester test.

Exam format

A 3-hour exam containing three sections: Multiple choice, Concepts and theory, and Applications and real-world data.

Final mark

Your final mark F in the paper will be calculated according to this formula:

F = max(E, 0.7E + 0.15A + 0.15T)


  • E is the Exam mark
  • A is the Assignments mark
  • T is the Tests mark

and all quantities are expressed as percentages.

Students must abide by the University’s Academic Integrity Policy

Academic integrity means being honest in your studying and assessments. It is the basis for ethical decision-making and behaviour in an academic context. Academic integrity is informed by the values of honesty, trust, responsibility, fairness, respect and courage.

Academic misconduct is seeking to gain for yourself, or assisting another person to gain, an academic advantage by deception or other unfair means. The most common form of academic misconduct is plagiarism.

Academic misconduct in relation to work submitted for assessment (including all course work, tests and examinations) is taken very seriously at the University of Otago.

All students have a responsibility to understand the requirements that apply to particular assessments and also to be aware of acceptable academic practice regarding the use of material prepared by others. Therefore it is important to be familiar with the rules surrounding academic misconduct at the University of Otago; they may be different from the rules in your previous place of study.

Any student involved in academic misconduct, whether intentional or arising through failure to take reasonable care, will be subject to the University’s Student Academic Misconduct Procedures which contain a range of penalties.

If you are ever in doubt concerning what may be acceptable academic practice in relation to assessment, you should clarify the situation with your lecturer before submitting the work or taking the test or examination involved.

Types of academic misconduct are as follows:


The University makes a distinction between unintentional plagiarism (Level One) and intentional plagiarism (Level Two).

  • Although not intended, unintentional plagiarism is covered by the Student Academic Misconduct Procedures. It is usually due to lack of care, naivety, and/or to a lack to understanding of acceptable academic behaviour. This kind of plagiarism can be easily avoided.
  • Intentional plagiarism is gaining academic advantage by copying or paraphrasing someone elses work and presenting it as your own, or helping someone else copy your work and present it as their own. It also includes self-plagiarism which is when you use your own work in a different paper or programme without indicating the source. Intentional plagiarism is treated very seriously by the University.

Unauthorised Collaboration

Unauthorised Collaboration occurs when you work with, or share work with, others on an assessment which is designed as a task for individuals and in which individual answers are required. This form does not include assessment tasks where students are required or permitted to present their results as collaborative work. Nor does it preclude collaborative effort in research or study for assignments, tests or examinations; but unless it is explicitly stated otherwise, each students answers should be in their own words. If you are not sure if collaboration is allowed, check with your lecturer..


Impersonation is getting someone else to participate in any assessment on your behalf, including having someone else sit any test or examination on your behalf.


Falsification is to falsify the results of your research; presenting as true or accurate material that you know to be false or inaccurate.

Use of Unauthorised Materials

Unless expressly permitted, notes, books, calculators, computers or any other material and equipment are not permitted into a test or examination. Make sure you read the examination rules carefully. If you are still not sure what you are allowed to take in, check with your lecturer.

Assisting Others to Commit Academic Misconduct

This includes impersonating another student in a test or examination; writing an assignment for another student; giving answers to another student in a test or examination by any direct or indirect means; and allowing another student to copy answers in a test, examination or any other assessment.

Further information

While we strive to keep details as accurate and up-to-date as possible, information given here should be regarded as provisional. Individual lecturers will confirm teaching and assessment methods.

Sunspot records were some of the data sets that stimulated research on statistical analysis of time series in the 20th century.

Here is the activity record from 1955 to 2000: