# MATU9MD - Time Series & Stochastic Processes

SCQF Level: 10
Course Prerequisite: MAT9K4
Credit Value: 20 (1 module)

### Aims

This module will provide a foundation for examining relationships between continuous variables. In particular, the techniques used when the explanatory variable is time will be presented and applied in a number of different subject areas (1/2). It will also acquaint the students with the theories of stochastic processes and their applications to a variety of different areas, including physics, and genetics (1/2).

### Learning Outcomes

Students should be able to: write down master equations for Markov processes and determine the average behaviour and variance, or solve them exactly; write down a stochastic matrix and use it to calculate the long term probability distribution between the states; interpret the description of a genetic model; analyse a gamblers ruin problem; write down the H theorem and prove it holds for a specific problem; analyse a branching chain problem; estimate a linear model to describe data and discuss the required assumptions; determine the appropriate transformation to linearise data; manipulate centred four point moving average data, choose the appropriate model to describe it (additive or multiplicative) and seasonally adjust the series in the appropriate way; derive the mean, covariance and correlation between time points of a general linear process, construct moving average and autoregressive models.

### Content

A1. Motivation & Graphical Description
A2. Regression Techniques
A3. Models for Stationary Time-Series
A4. Forecasting
B1. Probability functions and conditional probabilities
B2. Markov processes and chains
B3. Master equations and detailed balance

### Transferable Skills

The ability to formulate problems in mathematical terms; report writing; problem solving; information retrieval; interpretation of statistical information.

### Teaching Format

There will be three 1-hour lectures and one 1.5 hour practical per week.

### Assessment

1/3 coursework (1 practical project and 1 test) and 2/3 examination.

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