Financial Statistics

Financial statistics is related to the development of statistical techniques to analyse the time series of market prices and returns to investors. The Financial statistics group has a wide range of research activities. These include, in particular, developing robust estimation procedure for financial time-series, applying extreme value methods to measure the risk of a portfolio of investments and using modern statistical methods in credit-scoring.

About the Financial Statistics Group

Group members of Jon Tawn, Joe Whittaker and Kanchan Muhkerjee, together with a variety of research students.

Robust Estimation

Generalised autoregressive conditional heteroscedastic or GARCH models have been extensively used to understand the volatility or the instantaneous variability of a financial time series such as stock prices, exchange rates, interest rates etc. Volatility is related to the value at risk (VaR) which is a key measure for financial market risk. The current research of K. Mukherjee focuses on proposing and computing new, efficient and robust estimators of the parameters associated with volatility and VaR based on heteroscedastic GARCH models and to study them both theoretically and empirically on simulated and real data sets.

Portfolio Risk

Standard statistical models do not adequately describe the chance of large losses in a stock market investment. Extreme value methods have become widely used to model the heaviness of the tail of the loss distribution. When asessing the risk of large losses for a portfolio of investments the dependence between the losses in the individual investments is also of importance. Again standard statistical models fails to capture the range of observed dependence. Using novel methods for multivariate extreme values developed at Lancaster, coupled with knowledge of the structure of financial time series, we are developing methods for assessing portfolio risk and equivalently the selection of a portfolio to minimises losses.

Credit-Scoring

Credit scoring is an important tool for the financial services industry, used in all forms of consumer banking and insurance. More generally because of the revolution in e-database construction over the past two decades scoring has become the principal empirical tool for customer relations management in widely diverse fields, including marketing, retailing, and even for prioritisation in health services management. The theory for scoring derives from basic statistical techniques of regression and classification, and reduces the highly multivariate nature of consumer data to useful measures calibrated for prediction of future behaviour, such as credit default, repayment, churn, profit, bankruptcy, and fraud to take examples from credit card scoring.

The group at Lancaster has made theoretical developments in scorecard analysis, including the use of neglog transforms and quantile regression, and methods for detecting temporal shifts in population scores.

Recent Publications

• K. Mukherjee (2008). M-estimation in GARCH models. Econometric Theory, 24, 1530-1553.

• Whittaker, J., Whitehead C. and Somers, M. (2007). A dynamic scorecard for monitoring baseline performance: with application to tracking a mortgage portfolio. J. Operational Res.Soc., 58, 7, 911-921.
• Somers, M. and Whittaker, J. (2007). Quantile regression for modelling distributions of profit and loss. European Journal of Operational Research, 183, 1477-1487.
• K. Mukherjee (2007). Generalized R-estimators under Conditional heteroscedasticity. Journal of Econometrics, 141, 383-415.
• K. Mukherjee (2006). Pseudo-likelihood estimation in ARCH model. Canadian Journal of Statistics, 34, 341-356.