Raymond O'Brien

Numerically stable cointegration analysis

Cointegration analysis involves the solution of a generalized eigenproblem involving moment matrices and inverted moment matrices. These formulae are unsuitable for actual computations because the condition numbers of the resulting matrices are unnecessarily increased. The special structure of the cointegration procedure is used to achieve numerically stable computations, based on QR and singular value decompositions.

A violation of dominance and the consumption value of gambling

We document an apparently widespread violation of dominance in the horse-racing betting market in the UK, and use the systematic variation in the incidence of this violation to estimate the consumption value of gambling. Betting-shop gamblers in the UK face a tax on gambling of 10%, but have the choice of paying the tax either at the time of wager or on any return on a successful bet. It can be shown, however, that the latter act is strictly dominated by another action in which tax is paid on the wager. Despite this, more than 18% of bets appear to be placed by gamblers who choose to pay tax on the return. We explore the hypothesis that this apparent violation of rationality may be explained by a component of utility which represents the consumption value of gambling, which in turn varies with the amount wagered. We then estimate this component from a dataset consisting of a record of 25,000 individual bets using probit analysis of the tax decision.

Exact properties of the maximum likelihood estimator in exponential regression models: a differential geometric approach

Using recently developed methods for obtaining exact distribution results for implicitly defined estimators, we study the exact properties of the maximum likelihood estimator in exponential regression models. The main technical problem is the evaluation of a surface integral over an n-k)-dimensional hyperplane embedded in the n-dimensional sample space. Details of the calculation are given for the cases k = 1 and k = 2 and some general properties of the densities for arbitrary k are indicated.

Global macroeconomic shocks, time-varying covariances and tests of the international CAPM

The mean variance efficiency (MVE) of a portfolio of international bonds and equities is tested using a CAPM model of excess returns. The conditional variances and covariances of the portfolio returns are allowed to time-vary according to shocks in up to three global macro-economic variables simultaneously. Athough the hypothesis of MVE is easily rejected within a static version of the CAPM this is not the case at conventional significance levels in the CAPM with macro-economic shocks. Results suggest that there exists a dominant role for US macroeconomic disturbances for international capital markets. Integrating macro-economic disturbances more fully into the CAPM may provide theory-consistent models which do not rely solely upon time-series representations of time-varying return variances and covariances such as ARCH.