  Although many studies collect biomedical time series signals from multiple
subjects, there is a dearth of models and methods for assessing the association
between frequency domain properties of time series and other study outcomes.
This article introduces the random Cramer representation as a joint model for
collections of time series and static outcomes where power spectra are random
functions that are correlated with the outcomes. A canonical correlation
analysis between cepstral coefficients and static outcomes is developed to
provide a flexible yet interpretable measure of association. Estimates of the
canonical correlations and weight functions are obtained from a canonical
correlation analysis between the static outcomes and maximum Whittle likelihood
estimates of truncated cepstral coefficients. The proposed methodology is used
to analyze the association between the spectrum of heart rate variability and
measures of sleep duration and fragmentation in a study of older adults who
serve as the primary caregiver for their ill spouse.
