Bivariate Time Series Analysis of Longitudinal Models

• Activity Number: 257
• Type: Contributed
• Date/Time: Monday, August 2, 2010 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistics in Epidemiology
• Author(s): Paul Kolm*+ and Claudine Jurkovitz
• Companies: Christiana Care Health System and Christiana Care Health System
• Keywords: Time series ; cross-correlate

Abstract

Cross-correlation analysis is used to assess the relationship of bivariate time series, Xt (t = 1, 2, 3, . . . T) and Yt(t = 1, 2, 3, . . . T) where the interval between t and t+1 is constant. The cross-correlation between two pre-whitened (detrended) time series, y(t) and x(t) is defined as the covariance of x and y divided by the square root of the product of the variances of x and y at lag 0. If y(t) = bx(t-k) then a peak in correlation appears on the positive side of k if x leads y or a peak in correlation appears on the negative side of k if x lags y. Correlations on the negative side should be statistically zero, and significantly greater than zero on the positive side if x "leads" y. "Leads" is a necessary, but not sufficient condition for causality. In this study, we build mixed effect models of time series that are not equally spaced and cross-correlate the models.