Spectral analysis of unequally spaced sampled time series

Abstract

The diurnal excretion patterns of several electrolytes and urea were studied in 5 freely moving rats on an elemental diet (Vivonex) administered either orally or as a continuous intragastric feeding; the lights were on from 07.00–19.00 h and off from 19.00–07.00 h. During continuous feeding the diurnal rhythms persisted, although the amplitude was lower than during oral feeding. The maximum excretion rates of potassium, phosphate and urea all coincided under both feeding regimens. The time of the maximum calcium excretion rate coincided with that of sodium during oral feeding but not during continuous feeding. During continuous feeding the maximum calcium excretion rate shifted from 04.00 to 10.00 h. The diurnal excretion of magnesium during continuous feeding was abolished, possibly as a result of the low calcium intake. From this study it can be concluded that duringcontinuous intragastric feeding all of the studied excretion patterns persist, with the exception of magnesium, which indicates that these rhythms are not merely the result of the intermittent intake of food and minerals.     

Tapered empirical likelihood for time series data in time and frequency domains

We investigate data tapering in two formulations of empiricallikelihood for time series. One empirical likelihood is formedfrom tapered data blocks in the time domain and a second isbased on the tapered periodogram in the frequency domain. Limitingdistributions are provided for both empirical likelihood versionsunder tapering. Theoretical and simulation evidence indicatesthat a data taper improves the coverage accuracy of empiricallikelihood confidence intervals for time series parameters,such as means and correlations.     

Semiparametric models and inference for biomedical time series with extra-variation

Biomedical trials often give rise to data having the form of time series of a common process on separate individuals. One model which has been proposed to explain variations in such series across individuals is a random effects model based on sample periodograms. The use of spectral coefficients enables models for individual series to be constructed on the basis of standard asymptotic theory, whilst variations between individuals are handled by permitting a random effect perturbation of model coefficients. This paper extends such methodology in two ways: first, by enabling a nonparametric specification of underlying spectral behaviour; second, by addressing some of the tricky computational issues which are encountered when working with this class of random effect models. This leads to a model in which a population spectrum is specified nonparametrically through a dynamic system, and the processes measured on individuals within the population are assumed to have a spectrum which has a random effect perturbation from the population norm. Simulation studies show that standard MCMC algorithms give effective inferences for this model, and applications to biomedical data suggest that the model itself is capable of revealing scientifically important structure in temporal characteristics both within and between individual processes.