Time series forecasts and extra-model information

Often a forecaster has supplementary information (e.g. field reports or forecasts from another source) that cannot be included directly in a time series model. Especially interesting are cases where this information is given at time intervals that are different from those of the time series model forecasts. Previous authors have considered a numerical and a model-based statistical method for combining extra-model information of this type with ARIMA model forecasts. This paper extends both methods to vector ARMA model forecasts and dynamic regression (transfer function) model forecasts. It is also shown that a Lagrange multiplier numerical procedure arises as a special case of the model-based procedure. An empirical example is given.     

Forecasts of power-transformed series

Consider a time series transformed by an instantaneous power function of the Box-Cox type. For a wide range of fractional powers, this paper gives the relative bias in original metric forecasts due to use of the simple inverse retransformation when minimum mean squared error (conditional mean) forecasts are optimal. This bias varies widely according to the characteristics of the data. A fast algorithm is given to find this bias, or to find minimum mean squared error forecasts in the original metric. The results depend on the assumption that the forecast errors in the transformed metric are Gaussian. An example using real data is given.     

Krüppel requirement for knirps enhancement reflects overlapping gap gene activities in the Drosophila embryo

Segmental pattern formation in Drosophila proceeds in a hierarchical manner whereby the embryo is stepwise divided into progressively finer regions until it reaches its final metameric form. Maternal genes initiate this process by imparting on the egg a distinct antero-posterior polarity and by directing from the two polar centres the activities of the zygotic genes. The anterior system is strictly dependent on the product of the maternal gene bicoid (bcd), without which all pattern elements in the anterior region of the embryo fail to develop. The posterior system seems to lack such a morphogen. Rather, the known posterior maternal determinants simply define the boundaries within which abdominal segmentation can occur, and the process that actively generates the abdominal body pattern may be entirely due to the interactions between the zygotic genes. The most likely candidates among the zygotic genes that could fulfil the role of initiating the posterior pattern-forming process are the gap genes, as they are the first segmentation genes to be expressed in the embryo. Here we describe the interactions between the gap genes Krüppel (Kr), knirps (kni) and tailless (tll). We show that kni expression is repressed by tll activity, whereas it is directly enhanced by Kr activity. Thus, Kr activity is present throughout the domain of kni expression and forms a long-range protein gradient, which in combination with kni activity is required for abdominal segmentation of the embryo.     

Common variants in ZNF365 are associated with both mammographic density and breast cancer risk

High-percent mammographic density adjusted for age and body mass index is one of the strongest risk factors for breast cancer. We conducted a meta analysis of five genome-wide association studies of percent mammographic density and report an association with rs10995190 in ZNF365 (combined P = 9.6 × 10(-10)). Common variants in ZNF365 have also recently been associated with susceptibility to breast cancer.