This course introduces statistical modelling of time series data. The course focuses on the three main areas; (i) modelling trends and seasonal patterns; (ii) modelling short-term correlation; and (iii) predicting observations at future points in time.

Lectures: 20

Tutorials: 5

Practical: 2, 2-hour computer lab sessions

STATS4037 Time Series

STATS3TBC Statistics 3T: Time Series

120-minute, end-of-course examination (100%)

To introduce the concept of a time series, and discuss a range of descriptive methods for identifying features of interest.

To present a range of approaches for representing trends and seasonality in a time series, and to assess their relative merits.

To describe the theoretical properties of commonly used time series models.

To describe a range of approaches for predicting future values of a time series.

To show how to apply the techniques from the course to real time series data sets in the statistical package R.

By the end of this course students will be able to:

■ determine whether a time series exhibits any evidence of a trend, seasonality or short-term correlation;

■ define what it means for a time series to be stationary;

■ define the class of ARIMA probability models;

■ determine whether a particular model from the class of ARIMA models is stationary and invertible;

■ derive the mean, variance and autocorrelation function for a particular model from the class of ARIMA models;

■ determine an appropriate model for a data set from the class of ARIMA models;

■ predict future values for a given time series;

■ use the statistical package R to fit an appropriate time series model to a real data set that adequately captures any trend, seasonality and short-term correlation in the data;

■ define classes of pulse response and step response intervention models for time series with abrupt changes of behaviour

■ derive limit properties of a particular model from two considered classes of intervention models.

Students must submit at least 75% by weight of the components (including examinations) of the course's summative assessment.