Bias in the estimation of non‐linear transformations of the integrated variance of returns

Volatility models such as GARCH, although misspecified with respect to the data‐generating process, may well generate volatility forecasts that are unconditionally unbiased. In other words, they generate variance forecasts that, on average, are equal to the integrated variance. However, many applications in finance require a measure of return volatility that is a non‐linear function of the variance of returns, rather than of the variance itself. Even if a volatility model generates forecasts of the integrated variance that are unbiased, non‐linear transformations of these forecasts will be biased estimators of the same non‐linear transformations of the integrated variance because of Jensen's inequality. In this paper, we derive an analytical approximation for the unconditional bias of estimators of non‐linear transformations of the integrated variance. This bias is a function of the volatility of the forecast variance and the volatility of the integrated variance, and depends on the concavity of the non‐linear transformation. In order to estimate the volatility of the unobserved integrated variance, we employ recent results from the realized volatility literature. As an illustration, we estimate the unconditional bias for both in‐sample and out‐of‐sample forecasts of three non‐linear transformations of the integrated standard deviation of returns for three exchange rate return series, where a GARCH(1, 1) model is used to forecast the integrated variance. Our estimation results suggest that, in practice, the bias can be substantial. Copyright © 2006 John Wiley & Sons, Ltd.     

木槿（Hibiscus syriacusL.）耐盐变异体的选择

木槿愈伤组织耐盐细胞系是在含ＮａＣｌ的培养基上通过屡代选择产生的，在无盐培养其中进行几代继代培养后的愈伤组织，由其分化的芽以及脱分化增殖的愈伤组织均表现了耐盐性，木槿耐盐细胞由于对ＮａＣｌ的反应比未经选择的细胞积累了更多的Ｎ＾＋，Ｋ＾＋，而且细胞体积较小。     

Mutations in the gene encoding 11-cis retinol dehydrogenase cause delayed dark adaptation and fundus albipunctatus.

The metabolic pathways that produce 11-cis retinal are important for vision because this retinoid is the chromophore residing in rhodopsin and the cone opsins. The all-trans retinal that is generated after cone and rod photopigments absorb photons of light is recycled back to 11-cis retinal by the retinal pigment epithelium and Müller cells of the retina. Several of the enzymes involved have recently been purified and molecularly cloned; here we focus on 11-cis retinol dehydrogenase (encoded by the gene RDH5; chromosome 12q13-14; ref. 4), the first cloned enzyme in this pathway. This microsomal enzyme is abundant in the retinal pigment epithelium, where it has been proposed to catalyse the conversion of 11-cis retinol to 11-cis retinal. We evaluated patients with hereditary retinal diseases featuring subretinal spots (retinitis punctata albescens and fundus albipunctatus) and patients with typical dominant or recessive retinitis pigmentosa for mutations in RDH5. Mutations were found only in two unrelated patients, both with fundus albipunctatus; they segregated with disease in the respective families. Recombinant mutant 11-cis retinol dehydrogenases had reduced activity compared with recombinant enzyme with wild-type sequence. Our results suggest that mutant alleles in RDH5 are a cause of fundus albipunctatus, a rare form of stationary night blindness characterized by a delay in the regeneration of cone and rod photopigments.     

Global biodiversity patterns of marine phytoplankton and zooplankton

Although the oceans cover 70% of the Earth's surface, our knowledge of biodiversity patterns in marine phytoplankton and zooplankton is very limited compared to that of the biodiversity of plants and herbivores in the terrestrial world. Here, we present biodiversity data for marine plankton assemblages from different areas of the world ocean. Similar to terrestrial vegetation, marine phytoplankton diversity is a unimodal function of phytoplankton biomass, with maximum diversity at intermediate levels of phytoplankton biomass and minimum diversity during massive blooms. Contrary to expectation, we did not find a relation between phytoplankton diversity and zooplankton diversity. Zooplankton diversity is a unimodal function of zooplankton biomass. Most strikingly, these marine biodiversity patterns show a worldwide consistency, despite obvious differences in environmental conditions of the various oceanographic regions. These findings may serve as a new benchmark in the search for global biodiversity patterns of plants and herbivores.     

Spike train dynamics predicts theta-related phase precession in hippocampal pyramidal cells

According to the temporal coding hypothesis, neurons encode information by the exact timing of spikes. An example of temporal coding is the hippocampal phase precession phenomenon, in which the timing of pyramidal cell spikes relative to the theta rhythm shows a unidirectional forward precession during spatial behaviour. Here we show that phase precession occurs in both spatial and non-spatial behaviours. We found that spike phase correlated with instantaneous discharge rate, and processed unidirectionally at high rates, regardless of behaviour. The spatial phase precession phenomenon is therefore a manifestation of a more fundamental principle governing the timing of pyramidal cell discharge. We suggest that intrinsic properties of pyramidal cells have a key role in determining spike times, and that the interplay between the magnitude of dendritic excitation and rhythmic inhibition of the somatic region is responsible for the phase assignment of spikes.