MTH4230 · Time series and random processes in linear systems

Overview

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.

Areas of study: Applied mathematics Financial and insurance mathematics Mathematical statistics Mathematics

Offerings

Assessment

The Handbook lists an examination for this unit.

Assessment details may change. Please refer to the assessment information in Moodle closer to the start of the teaching period.

Requisites

The Handbook lists no prerequisite, corequisite or prohibition for this unit.

Learning outcomes

1. Analyse and evaluate stationary time series models, including autoregressive and moving average processes, and apply projection methods for forecasting;
2. Perform time and frequency domain analysis of time series data, applying techniques such as the Kalman filter and using ITSM to interpret and evaluate results;
3. Integrate theoretical understanding with practical implementation by applying stochastic models and computational tools to real data problems;
4. Extend and deepen understanding of time series methods through advanced model synthesis, rigorous analysis, and independent application to complex or novel datasets.
5. Apply the Kalman filter to random systems, demonstrating proficiency in both theoretical understanding and practical implementation.
6. Conduct analysis of time series data using the ITSM package, showcasing the ability to handle complex datasets and derive meaningful insights

Workload

Three 1-hour seminars; One 2-hour applied class (in weeks 2-12) and 7 hours of independent study per week.

Student experience, not official rules. Nothing here changes what the Handbook says.