ST959-15 Financial Statistics

Introductory description

This module runs in Term 1 and aims to introduce the main approaches to statistical inference and financial time series.

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 (weeks 1-5)

• 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 (weeks 6-10)

• 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

.

Transferable skills

.