### Introduction

Welcome to the module on Financial Econometrics. The first objective of this module is to introduce the main econometric methods and techniques used in the analysis of issues related to finance. A module with the title *Financial Econometrics* assumes that such a field exists.

In this module, we define financial econometrics as ‘the application of statistical techniques to problems in finance’. Although econometrics is often associated with analysing economics problems such as economic growth, consumption and investment, the applications in the areas of finance have grown rapidly in the last few decades.

Before starting this module, we recommend that you first complete the modules Econometric Principles and Data Analysis and Econometric Analysis and Applications.

### Learning outcomes

By the end of this module you will be able to:

- define and compute measures of financial returns
- interpret sample moments of financial returns
- discuss the stylised statistical properties of asset returns
- formulate models using matrix notation
- derive the OLS estimators using matrix algebra
- use matrix algebra to analyse sources of variation of risk
- explain the principles of maximum likelihood estimation
- derive the maximum likelihood estimators and discuss their properties
- use maximum likelihood estimation, and apply the hypothesis tests available under maximum likelihood estimation
- analyse and estimate models of autoregressive, moving average, and autoregressive-moving average models
- forecast using AR, MA, and ARMA models
- apply the Box-Jenkins approach to time series models
- model and forecast volatility using autoregressive conditional heteroscedastic (ARCH) models
- estimate, interpret, and forecast with generalised autoregressive conditional heteroscedastic (GARCH) models
- extend GARCH models to analyse the asymmetric effect of shocks on volatility
- construct, estimate and interpret multivariate GARCH models
- test for spill-over of volatility between assets
- use vector autoregressive (VAR) models to analyse and interpret interaction between financial variables
- examine the impact of shocks on financial variables using impulse response analysis
- undertake tests of hypotheses and Granger causality in a VAR framework
- formulate limited dependent variable models, including logit and probit models
- estimate and interpret logit and probit models
- discuss models with multinomial linear dependent variables.

### Study resources

###### Study guide

The module study guide is carefully structured to provide the main teaching, defining and exploring the main concepts and issues, locating these within current debate and introducing and linking the assigned readings.

###### Key texts

Brooks C (2019) Introductory Econometrics for Finance. 4th Edition. Cambridge UK: Cambridge University Press.

###### Econometric software

This module will use R. This is a widely used programming environment for data analysis and graphics. You will use this software to do the exercises in the units. The results presented in the units are also from R.

###### Readings

You will receive access to a selection of key academic articles which apply the techniques studied in the module to financial data.

###### Virtual learning environment

You will have access to the VLE, which is a web-accessed study centre. Via the VLE, you can communicate with your assigned academic tutor, administrators and other students on the module using discussion forums. The VLE also provides access to the module Study Guide and assignments, as well as a selection of electronic journals available on the University of London Online Library.

### Module overview

##### Unit 1 Statistical Properties of Financial Returns

- 1.1 Introduction
- 1.2 Calculation of Asset Returns
- 1.3 Stylised Facts about Financial Returns
- 1.4 Distribution of Asset Returns
- 1.5 Time Dependency
- 1.6 Linear Dependency across Asset Returns

##### Unit 2 Matrix Algebra, Regression and Applications in Finance

- 2.1 Introduction
- 2.2 Matrix Algebra: Some Basic Concepts and Applications
- 2.3 OLS Regression Using Matrix Algebra
- 2.4 Applications to Finance

##### Unit 3 Maximum Likelihood Estimation

- 3.1 Introduction
- 3.2 The Maximum Likelihood Function: Some Basic Ideas and Examples
- 3.3 The Maximum Likelihood Method: Mathematical Derivation
- 3.4 The Information Matrix
- 3.5 Usefulness and Limitations of the Maximum Likelihood Estimator
- 3.6 Hypothesis Testing

##### Unit 4 Univariate Time Series and Applications to Finance

- 4.1 Introduction
- 4.2 The Lag Operator
- 4.3 Some Key Concepts
- 4.4 Wold's Decomposition Theory (Optional section)
- 4.5 Properties of AR Processes
- 4.6 Properties of Moving Average Processes
- 4.7 Autoregressive Moving Average (ARMA) Processes
- 4.8 The Box-Jenkins Approach
- 4.9 Example: A Model of Stock Returns
- 4.10 Conclusions

##### Unit 5 Modelling Volatility – Conditional Heteroscedastic Models

- 5.1 Introduction
- 5.2 ARCH Models
- 5.3 GARCH Models
- 5.4 Estimation of GARCH Models
- 5.5 Forecasting with GARCH Model
- 5.6 Asymmetric GARCH Models
- 5.7 The GARCH-in-Mean Model
- 5.8 Conclusions

##### Unit 6 Modelling Volatility and Correlations – Multivariate GARCH Models

- 6.1 Introduction
- 6.2 Multivariate GARCH Models
- 6.3 The VECH Model
- 6.4 The Diagonal VECH Model
- 6.5 The BEKK Model
- 6.6 The Constant Correlation Model
- 6.7 The Dynamic Correlation Model
- 6.8 Estimation of a Multivariate Model

##### Unit 7 Vector Autoregressive Models

- 7.1 Introduction
- 7.2 Vector Autoregressive Models
- 7.3 Issues in VAR
- 7.4 Hypothesis Testing in VAR
- 7.5 Example: Money Supply, Inflation and Interest Rate

##### Unit 8 Limited Dependent Variable Models

- 8.1 Introduction
- 8.2 The Linear Probability Model
- 8.3 The Logit Model
- 8.4 The Probit Model
- 8.5 Estimation using Maximum Likelihood
- 8.6 Goodness of Fit Measures
- 8.7 Example: Dividends, Growth and Profits
- 8.8 Multinomial Linear Dependent Variables
- 8.9 Ordered Response Linear Dependent Variable Models (optional section)

### Tuition and assessment

Students are individually assigned an academic tutor for the duration of the module, with whom you can discuss academic queries at regular intervals during the study session.

You are required to complete two Assignments for this module, which will be marked by your tutor. Assignments are each worth 15% of your total mark. You will be expected to submit your first assignment by the Tuesday of Week 6, and the second assignment at the end of the module, on the Tuesday after Week 10. Assignments are submitted and feedback given online. In addition, queries and problems can be answered through the Virtual Learning Environment.

You will also sit a three-hour examination on a specified date in September/October, worth 70% of your total mark. An up-to-date timetable of examinations is published on the website in July each year.

### Module sample

Click on the link below to download the module sample document in PDF.