Abstract

Multivariate time series data are commonly observed in biomedical studies. Traditionally, the associations among different outcomes are modeled through functions of time, such as vector autoregressive models and multivariate spline models. However, in some situations, the regression-type associations between one time series and other time series are of interest, which can be either parametric or nonparametric. Two main challenges in modeling such regression-type associations are 1) that the autocorrelations in the outcome time series need to be accounted for with heavy computational burdens, and 2) the independent variable time series are observed with autocorrelated errors. We propose to use B-splines to model the potentially nonparametric regression-type associations and represent the model in state space forms. Consequently, Kalman filtering algorithms are adopted to efficiently handle the autocorrelated errors in the dependent time series. The errors in the independent variable time series are handled by multiple draws from their smoothed state vectors. Simulation is conducted to evaluate the finite sample performance. A surgery monitoring data example is used to illustrate the real-world application.