Stationarity; linear processes; AR and MA models Autocorrelation and autovariance for AR and MA processes.
Yule-Walker equations; causality and parameter reduction Estimation: Y-W equations, Method of moments for AR(1) and AR(2) models, Method of moments for MA(1) model. Least squares estimation for AR(1) and AR(2) models Best linear prediction for AR(2) models, Maximum Likelihood. ARCH/GARCH models, their estimation and generalisations; time series diagnostics for Öt.
State space form models; the Kalman Ölter and smoother; partitioned matrices for Gaussian densities. Stochastic volatility alternatives to the GARCH class and diagnostics; moment generating functions, estimation. Bayesian analysis via Markov chains
5CCM241A/6CCM241B Probability and Statistics II. If taking this module you are advised to also take Statistical Modelling 5CCM242A or 6CCM242B (may be taken simultaneously)
Educational aims & objectives
This module introduces the analysis of time series, i.e. series of observations evolving in time and observed at discrete points in time. The module considers both theoretical and applied aspects of time series. For the applied part, data will be examined using the software package R.
On successful completion of this module students will:
- have a technical understanding of time series methods
- be able to define concepts such as stationarity and non-stationarity
- be able to verify properties of particular models, e.g. ARMA(1,1) models
- be able to use the software package R to fit and apply several models to data
- be able to perform a statistical analysis of real data and interpret the results.
Three hours of lectures and one hour of tutorial per week throughout the term