MTH3230 - Time series and random processes in linear systems - 2018

6 points, SCA Band 2, 0.125 EFTSL

Undergraduate - Unit

Refer to the specific census and withdrawal dates for the semester(s) in which this unit is offered.



Organisational Unit

School of Mathematical Sciences

Chief examiner(s)

Associate Professor Tianhai Tian


Associate Professor Tianhai Tian

Unit guides



  • Second semester 2018 (On-campus)


Students must be enrolled in the Master of Financial Mathematics or have passed one of the following units: MTH2010, MTH2015, MTH2032, MTH2040, MTH2222 OR ENG2005. MTH2222 is highly recommended.


Multivariate distributions. Estimation: maximum of likelihood and method of moments. Confidence intervals. Analysis in the time domain: stationary models, autocorrelation, partial autocorrelation. ARMA and ARIMA models. Analysis in the frequency domain (Spectral analysis): spectrum, periodigram, linear and digital filters, cross-correlations and cross-spectrum, spectral estimators, confidence interval for the spectral density. State-space models. Kalman filter. Empirical Orthogonal Functions and other Eigen Methods. Use of ITSM.


On completion of this unit students will be able to:

  1. Articulate the concept of stationary time series;
  2. Manipulate the concept of projection and its use in forecasting;
  3. Understand the models of autoregression and moving averages and their combinations;
  4. Analyse time series in time domain as well as frequency domain;
  5. Apply the Kalman filter to random systems;
  6. Analyse time series data using the ITSM package.


Examination (3 hours): 60% (Hurdle)

Continuous assessment: 40%

Hurdle requirement: To pass this unit a student must achieve at least 50% overall and at least 40% for the end-of-semester exam.

Workload requirements

Three 1-hour lectures and one 2-hour support class per week

See also Unit timetable information

This unit applies to the following area(s) of study