MA5507 (Mathematical Statistics) or equivalent
OverviewA time series is a collection of observations made sequentially in time. Examples occur in a variety of fields, ranging from economics to engineering, and methods of analysing time series constitute an important area of statistics. This module focuses initially on various time series models, including some recent developments, and provides modern statistical tools for their analysis. The second part of the module covers extensively simulation methods. These methods are becoming increasingly important tools as simulation models can be easily designed and run on modern PCs. Various practical examples are considered to help students tackle the analysis of real data.The syllabus includes: Difference equations, Stationary Time Series: ARMA process. Nonstationary Processes: ARIMA Model Building and Testing: Estimation, Box Jenkins, Criteria for choosing between models, Diagnostic tests.Forecasting: Box-Jenkins, Prediction bounds. Testing for Trends and Unit Roots: Dickey-Fuller, ADF, Structural change, Trend-stationarity vs difference stationarity. Seasonality and Volatility: ARCH, GARCH, ML estimation. Multiequation Time Series Models: Spectral Analysis. Generation of pseudo random numbers, simulation methods: inverse transform and acceptance-rejection, design issues and sensitivity analysis.
Marks on this module can count towards exemption from the professional examination CT6 of the Institute and Faculty of Actuaries. Please see http://www.kent.ac.uk/casri/Accreditation/index.html for further details.
This module appears in:
Method of assessment
90% Examination, 10% Coursework
PJ Brockwell & RA Davis Introduction to Time Series and Forecasting. (Springer. 2nd.ed.2002) (R)
W Enders Applied Econometric Time Series (Wiley. 2nd Ed., 2004) (R)
BJT Morgan Elements of Simulation, Chapman and Hall, 1984
The intended subject specific learning outcomes
On successful completion of this module students will:
a) have a good understanding of processes underlying time series data;
b) be able to apply with some theoretical justification the time series techniques encountered in various applications;
c) gain a good knowledge of various methods for generating random numbers;
d) have a reasonable ability to solve a variety of practical problems to which simulation techniques can be applied.
The intended generic learning outcomes
Students who successfully complete this module will:
a) have further developed a logical, mathematical approach to solving problems;
b) have enhanced their ability to work with relatively little guidance;
c) be able to use information technology for data retrieval , data analysis and presentation;
d) have gained further organisational and interpretational skills.
On successful completion of this module, students will also have improved their key skills in written communication, numeracy and problem solving.