Introductory description

This module aims to introduce the main approaches to statistical inference and financial time series.

Module web page

Module aims

Outline syllabus

This is an indicative module outline only to give an indication of the sort of topics that may be covered. Actual sessions held may differ.

Part 1: Classical and Bayesian methods of statistical inference

• Properties of random samples
• Statistics, sufficiency and likelihood
• Point estimation, maximum likelihood estimation
• Hypothesis testing and interval estimation
• Elements of Bayesian inference
• Linear models

Part 2: Time Series

• Auto-regressive and moving average models (ARMA), unit root (ARIMA) and seasonal models (S-ARIMA), heteroscedastic models (GARCH and extensions such as EGARCH, GARCH-M,...) and an introduction to stochastic volatility models.
• Linear and non-linear modelling of financial time series with R: exploratory analysis, model selection, model fitting, model validation and forecasting.
• Illustrative financial applications.

Learning outcomes

By the end of the module, students should be able to:

• Explain the different approaches of statistical inference for points estimation, hypothesis testing and confidence set construction.
• Apply linear models in general situations and perform ANOVA.
• Understand and critically analyse ARMA, unit root, S-ARIMA, and GARCH models. Apply these models to financial data and carry out relevant computations.
• Demonstrate an understanding of the generalised linear model, including an appreciation of the circumstances where it may or may not be applied and, where appropriate, good judgement of where to apply it.

Indicative reading list

Part 1

• George Casella, Roger Berger: Statistical Inference, (2002) Cengage Learning; 2nd edition
• David Ruppert and David S. Matteson: Statistics and Data Analysis for Financial Engineering: with R examples, Springer; 2nd edition
• Larry A. Wasserman: All of Statistics: A Concise Course in Statistical Inference, Springer

Part 2

• Jonathan D. Cryer and Kung-Sik Chan: (2008) Time Series Analysis: With applications in R, Spinger, 2nd edition
• David Ruppert and David S. Matteson: (2015) Statistics and Data Analysis for Financial Engineering: with R examples, Springer; 2nd edition
• Ruey S Tsay: (2010) Analysis of Financial times series, Wiley; 3rd edition
• Financial Econometrics by Christian Gourieroux and Joann Jasiak, Princeton University Press.

View reading list on Talis Aspire

Subject specific skills

• Demonstrate facility with rigorous probabilistic methods.

• Evaluate, select and apply appropriate mathematical and/or probabilist techniques.

• Demonstrate knowledge of and facility with formal probability concepts, both explicitly and by applying them to the solution of finance problems.

• Create structured and coherent arguments communicating them in written form. 

• Construct logical mathematical arguments with clear identification of assumptions and conclusions.
  Reason critically, carefully, and logically and derive (prove) mathematical results.

Transferable skills

• Problem solving: Use rational and logical reasoning to deduce appropriate and well-reasoned conclusions. Retain an open mind, optimistic of finding solutions, thinking laterally and creatively to look beyond the obvious. Know how to learn from failure.

• Self awareness: Reflect on learning, seeking feedback on and evaluating personal practices, strengths and opportunities for personal growth.

• Communication: Present arguments, knowledge and ideas, in a range of formats.

• Professionalism: Prepared to operate autonomously. Aware of how to be efficient and resilient. Manage priorities and time. Self-motivated, setting and achieving goals, prioritising tasks.