Gestational vitamin D insufficiency is related with increased risks of various diseases and poor health outcomes later in life. Telomere length at birth or early in life is known to be a predictor of individual health. Both vitamin D and telomere length are related with various health conditions, and vitamin D concentrations are associated with leukocyte telomere lengths in women.We investigated the association between maternal vitamin D concentrations and newborn leukocyte telomere lengths. This cross-sectional study included 106 healthy pregnant women without adverse obstetric outcomes and their offspring. We examined the maternal age, weight before pregnancy, health behaviours, and nutritional intakes, along with each newborn's sex and birthweight, and we measured maternal height, telomere length, total white blood cell count, and glycosylated haemoglobin as covariates. Pearson's correlation coefficients were calculated to evaluate the relationship between the baseline variables and newborn leukocyte telomere lengths. To confirm that there was an independent association between newborn leukocyte telomere lengths and maternal vitamin D concentrations, we performed a stepwise multiple linear regression analysis. Newborn leukocyte telomere lengths correlated positively with maternal leukocyte telomere lengths (r = .76, p < .01), maternal 25-hydroxyvitamin D concentrations (r = .72, p < .01), maternal energy intakes (r = .22, p = .03), and newborn body weights (r = .51, p < .01). In the multivariate model, newborn leukocyte telomere lengths were associated with maternal vitamin D concentrations (β = .33, p < .01). These findings suggest that the maternal vitamin D concentration during pregnancy may be a significant determinant of the offspring's telomere length.

We develop a method for directly modeling cointegrated multivariate time series that are observed in mixed frequencies. We regard lower-frequency data as regularly (or irregularly) missing and treat them with higher-frequency data by adopting a statespace model. This utilizes the structure of multivariate data as well as the available sample information more fully than the methods of transformation to a single frequency, and enables us to estimate parameters including cointegrating vectors and the missing observations of low-frequency data and to construct forecasts for future values. For the maximum likelihood estimation of the parameters in the model, we use an expectation maximization algorithm based on the state-space representation of the error correction model. The statistical efficiency of the developed method is investigated through a Monte Carlo study. We apply the method to a mixedfrequency data set that consists of the quarterly real gross domestic product and the monthly consumer price index.JEL classification: C13, C22, C32.

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An extension of Gaussian reduced rank estimation of Ahn and Reinsel (Journal of Econometrics, Vol. 62, pp. 317-350, 1994) to seasonal periods other than four is presented. Simple adjustments for estimation that are necessary because of complex-valued seasonal unit roots are presented in detail and the asymptotic distribution of the estimators that takes the same form as that in Ahn and Reinsel (1994) is derived. Tests for contemporaneous cointegration and common polynomial cointegrating vectors (PCIVs) for different seasonal unit roots are presented. Finite sample properties are briefly examined through a small Monte Carlo simulation study and a numerical example is presented to illustrate the methods.

The maximum eigenvalue (ME) test for seasonal cointegrating ranks is presented using the approach of Cubadda [Oxford ]. The asymptotic distributions of the ME test statistics are obtained for several cases that depend on the nature of deterministic terms. Monte Carlo experiments are conducted to evaluate the relative performances of the proposed ME test and the trace test, and we illustrate these tests using a monthly time series.