Title: A frequency-domain multivariate linear model for analyzing multiple time series and covariates
Authors: Zeda Li - City University of New York (United States) [presenting]
Yuexiao Dong - Temple University (United States)
Abstract: A frequency-domain multivariate linear model is proposed to study the association between covariates and the second-order power spectra of multiple time series. A random Cramer representation, where power spectra are assumed to be random functions that are correlated with the covariates, is used as a joint model for collections of time series and covariates. Each subject-specific time series is represented by a set of cepstral coefficients, allowing the proposed model to capture frequency patterns of the time series parsimoniously. A multivariate linear model concerning the cepstral coefficients and covariates is then constructed to provide flexible yet interpretable measures of association between power spectra and covariates. The parameters of the multivariate linear model can be estimated by the envelope estimator, which provides a tool for dimension reduction and is more robust than the ordinary least squares estimator when the covariates are highly correlated. Empirical performance is evaluated in simulation studies and illustrated through a study of gait variability in young children.