Hierarchical time-varying mixed-effects models in high-dimensional time series and longitudinal data studies

Abstract

ABSTRACT We propose time-varying coefficient mixed-effects models for continuous multiple time series data and longitudinal data. The challenge is how to simultaneously display serial, clustering, and multivariate attributes of the data set, to which the routinely assumed two-level hierarchical model and univariate response models are not able to apply. Asymptotic properties of the proposed methods are established. We also conduct the model comparison, and find that the proposed methods outperform the traditional univariate response models, nonparametric models, and linear mixed effects models in both predicting the response and estimating the coefficient surface based on simulation studies. Finally, we have applied our methods to a real-world study on the price–volume relationship of NASDAQ stock market data.