Introduction

There have been numerous empirical analyses of the efficient markets hypothesis when applied to gambling markets (see, e.g., Sauer, 1998, and Vaughan Williams, 1999, for recent comprehensive surveys). The literature suggests that the null of market efficiency – at least where risk-neutrality is assumed – can be consistently rejected in three major areas of research application. However many of the rejections of the restrictions, required by the efficiency hypothesis, that are reported in the literature are based on classical least-squares regression procedures even though the regression residuals exhibit sometimes very pronounced deviations from normality and heteroscedasticity. As a consequence the inferences based on classical methods are suspect as the true size of the relevant test statistics is not the one hypothesised. Our purpose in this chapter is to reconsider some of the violations of efficiency, employing recently suggested bootstrap estimation procedures which allow for heteroscedasticity and any non-normality in OLS regression residuals. The procedures we employ might be found useful by other researchers in the area. At least they allow for more robust statistical inference than has hitherto often been the case. The chapter is organised as follows. In section 17.2 we first set out the wild bootstrap and then apply the wild bootstrap on a variety of datasets (sections 17.3 - 17.5). Section 17.6 draws some conclusions.

The bootstrap methods, statistical inference

Recent advances in computing offer an alternative approach to hypothesis testing when the error term in a regression is heteroscedastic and potentially non-normal.