Estimating the Ozone Depletion Potential of Methyl Bromide

Ozone depletion potential (ODP) represents the cumulative ozone depletion induced by a particular halocarbon relative to a reference gas (usually trichlorofluoromethane, CFC-11). We focus on ODP estimation for methyl bromide. Previous attempts at its estimation have assumed that components of the ODP equation are lognormally distributed. By considering a wide range of modeling scenarios, we show that this restriction (which is based on computational convenience rather than experimental evidence) has obscured the true uncertainty in the ODP value. Moreover, when publishing point estimates for the ODP value, previous authors have given either mean or median values. We submit that a more appropriate choice for a point estimate is the mode since the distribution of ODP is skewed and since the mode is by definition, the most likely value. For each modeling scenario considered, modal values are given. In general, we find these ODP point estimates are considerably lower than those published elsewhere.     

A Bootstrap Stationarity Test for Predictive Regression Invalidity

In order for predictive regression tests to deliver asymptotically valid inference, account has to be taken of the degree of persistence of the predictors under test. There is also a maintained assumption that any predictability in the variable of interest is purely attributable to the predictors under test. Violation of this assumption by the omission of relevant persistent predictors renders the predictive regression invalid, and potentially also spurious, as both the finite sample and asymptotic size of the predictability tests can be significantly inflated. In response, we propose a predictive regression invalidity test based on a stationarity testing approach. To allow for an unknown degree of persistence in the putative predictors, and for heteroscedasticity in the data, we implement our proposed test using a fixed regressor wild bootstrap procedure. We demonstrate the asymptotic validity of the proposed bootstrap test by proving that the limit distribution of the bootstrap statistic, conditional on the data, is the same as the limit null distribution of the statistic computed on the original data, conditional on the predictor. This corrects a long-standing error in the bootstrap literature whereby it is incorrectly argued that for strongly persistent regressors and test statistics akin to ours the validity of the fixed regressor bootstrap obtains through equivalence to an unconditional limit distribution. Our bootstrap results are therefore of interest in their own right and are likely to have applications beyond the present context. An illustration is given by reexamining the results relating to U.S. stock returns data in Campbell and Yogo (2006 Campbell, J. Y. and Yogo, M. (2006), “Efficient Tests of Stock Return Predictability,” Journal of Financial Economics, 81, 27–60.[Crossref], [Web of Science ®] , [Google Scholar]). Supplementary materials for this article are available online.     

Wild Bootstrap of the Sample Mean in the Infinite Variance Case

It is well known that the standard independent, identically distributed (iid) bootstrap of the mean is inconsistent in a location model with infinite variance (α-stable) innovations. This occurs because the bootstrap distribution of a normalised sum of infinite variance random variables tends to a random distribution. Consistent bootstrap algorithms based on subsampling methods have been proposed but have the drawback that they deliver much wider confidence sets than those generated by the iid bootstrap owing to the fact that they eliminate the dependence of the bootstrap distribution on the sample extremes. In this paper we propose sufficient conditions that allow a simple modification of the bootstrap (Wu, 1986 Wu , C. F. J. ( 1986 ). Jackknife, bootstrap, and other resampling methods . Annals of Statistics 14 : 1261 – 1295 .[Crossref], [Web of Science ®] , [Google Scholar]) to be consistent (in a conditional sense) yet to also reproduce the narrower confidence sets of the iid bootstrap. Numerical results demonstrate that our proposed bootstrap method works very well in practice delivering coverage rates very close to the nominal level and significantly narrower confidence sets than other consistent methods.     

Cross-cumulants measure for independence

We propose a measure for independence of group of random variables, given by a sum of cross-cumulants of a given order n  . A similar measure was known for the case of fourth-order cross-cumulants from the JADE algorithm for ICA (independent component analysis). We derive a formula for its calculation using cumulant tensors. In the case n=4$n=4$ our formula allows efficient calculation of this measure, using cumulant matrices. Much attention is devoted to the case of six-order cross-cumulants, aiming to show that this measure can be calculated using again cumulant matrices.