# Statistics MSc

## Time Series (Level M) STATS5030

• School: School of Mathematics and Statistics
• Credits: 10
• Level: Level 5 (SCQF level 11)
• Typically Offered: Semester 2
• Available to Visiting Students: Yes

### Short Description

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.

### Timetable

Lectures: 20

Tutorials: 5

Practical: 2, 2-hour computer lab sessions

### Excluded Courses

STATS4037 Time Series

STATS3TBC Statistics 3T: Time Series

### Assessment

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

Main Assessment In: April/May

### Course Aims

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.

### Intended Learning Outcomes of Course

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.

### Minimum Requirement for Award of Credits

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