Undergraduate - UnitMTH3230 - Time series and random processes in linear systems

This unit entry is for students who completed this unit in 2015 only. For students planning to study the unit, please refer to the unit indexes in the the current edition of the Handbook. If you have any queries contact the managing faculty for your course or area of study.

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6 points, SCA Band 2, 0.125 EFTSL

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

Level	Undergraduate
Faculty	Faculty of Science
Organisational Unit	School of Mathematical Sciences
Offered	Clayton Second semester 2015 (Day)
Coordinator(s)	Professor Fima Klebaner

Synopsis

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.

Outcomes

On completion of this unit students will be able to:

Appreciate the concept of stationary time series;

Understand the concept of projection and its use in forecasting;

Understand the models of autoregression and moving averages and their combinations;

Analyse time series in time domain as well as frequency domain;

Understand the model of Kalman filter;

Use the package ITSM to analyse time series data.

Assessment

Final examination (3 hours): 70%
Assignments, tests and participation in tutorials: 30%

Workload requirements

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

Chief examiner(s)

Professor Fima Klebaner

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

Atmospheric science
Mathematics and statistics

Prerequisites

One of MTH2010, MTH2015, MTH2032 or MTH2222. MTH2222 is highly recommended.