Nonlinear estimation and statistical testing of periods in nonsinusoidal longitudinal time series with unequidistant observations

The analysis of multiple components is often used to model biological varia bles that show nonsinusoidal predictable changes of known periods. In gener al, to anticipate the periods is not easy, and even in cases when we have s ome a priori information, it is advisable to have a statistical tool to tes t the chosen periods. In this work, we introduce a statistical procedure to estimate periods of longitudinal series by applying nonlinear regression t echniques to the multiple sinusoidal model, as well as to the general linea r model. Approximate inferences about the parameters of the model are carri ed out under the usual hypothesis of normality, independence, and constant variance of the errors. Confidence intervals (CIs) for each individual para meter, as well, as for the amplitude-acrophase pair or for any other subgro up of parameters of interest, can be computed. As in the linear analysis of multiple components, it is possible to check the existence of rhythm by me ans of a zero-amplitude test. The method also allows statistical testing of several hypotheses related to the periods. For example, it is possible to test if the periods are equal to certain values of chronobiologic interest and to check if some components included in the model are harmonically rela ted. On the other hand, when the fitted components have proximal periods, t he method allows one to verify if they are modeling the same or different s pectral peaks. The method, which was validated by a simulation study for a model of two components and is illustrated by an example of modeling the di astolic blood pressure of two subjects, represents a new step in the develo pment of statistical procedures in chronobiology.