# Statistical Methods and Time Series Analysis

## Course summary

Course code: STAT1027
Level: 5
Credits: 30
School: Architecture, Computing and Hums
Department: Mathematical Sciences
Course Coordinator(s): Nadarajah Ramesh / Ana Paula Palacios

## Specification

### Pre and co requisites

Probability and Statistical Analysis.

### Aims

It is important to have an understanding and the skill in the application of the widely used statistical methods & techniques for analysing real-life data sets. The aim of the course is to help students develop knowledge in areas such as Bivariate Distributions, Regression analysis, Analysis of Variance, and Time Series analysis which play a large role in decision making (via data analysis) on problems arising in business, industry, and other scientific and educational situations. This course also provides students with knowledge and understanding of methods used in the analysis of time related data and introduces them to the area of Markov chains.

### Learning outcomes

On successful completion of this course a student will be able to:

1. Demonstrate abilities in dealing with bi-variate distributions, marginal and conditional distributions; independence & functions of random variables.
2. Choose appropriate simple and multiple linear regression models and carry out the required analysis and reflect on results.
3. Recognise & perform various ANOVA and evaluate their results; perform data analysis using appropriate dummy variable regression models and interpret the results.
4. Make a choice of appropriate statistical methods to analyse time series data & other time related data. Perform exponential smoothing of time series data and make forecasts.
5. Demonstrate an understanding of Markov chains and their application to time-related data analysis in other field and appreciate disciplines and forms of professional practice beyond Statistics and draw connections between them.
6. Use statistical packages on realistic data sets, interpret computer outputs of their analysis and report on findings.

### Indicative content

Simple and multiple linear regressions, dummy variable regression models; Inference and Prediction for multiple regressions: ANOVA table, testing of significance, inference for coefficients, confidence intervals & prediction intervals; Bivariate discrete distributions, marginal and conditional distributions, mean and variance, covariance and correlation, independence; Analysis of Variance (One-way & Two-way); Time Series Analysis; Decomposition methods using additive and multiplicative models; Simple exponential smoothing. Holtâ€™s 2-parameter method. Holt-Winters 3-parameter method; Lagged regression models for time series. Sample autocorrelation function. Durbin-Watson test; AR and MA processes and Introduction to Markov Chains.

### Teaching and learning activity

Concepts, methods and basic conclusions will be introduced and explained in lectures.
Problem solving and technique training will be done through tutorials.
Practical work using statistical software will be done through laboratory sessions.

### Assessment

Summative assessment:
Coursework 1 - 25%
An individual coursework assessing learning outcomes 1,2,3

Coursework 2 - 25%
An individual coursework assessing learning outcomes 3,4,6

Exam - 50%
A 3-hour long examination assessing all learning outcomes, LO - 1-6.

Formative assessment: Weekly tutorial exercises.