Generation and annotation of the DNA sequences of human chromosomes 2 and 4

Human chromosome 2 is unique to the human lineage in being the product of a head-to-head fusion of two intermediate-sized ancestral chromosomes. Chromosome 4 has received attention primarily related to the search for the Huntington's disease gene, but also for genes associated with Wolf-Hirschhorn syndrome, polycystic kidney disease and a form of muscular dystrophy. Here we present approximately 237 million base pairs of sequence for chromosome 2, and 186 million base pairs for chromosome 4, representing more than 99.6% of their euchromatic sequences. Our initial analyses have identified 1,346 protein-coding genes and 1,239 pseudogenes on chromosome 2, and 796 protein-coding genes and 778 pseudogenes on chromosome 4. Extensive analyses confirm the underlying construction of the sequence, and expand our understanding of the structure and evolution of mammalian chromosomes, including gene deserts, segmental duplications and highly variant regions.     

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.