Coherence Consideration in Binary Time Series Analysis

In a recent study of mortality forecasting in the United States, it has been found that quite often mortality patterns in a given state are influenced by mortality trends in neighboring states, and the inclusion of interaction terms from the latter in log-linear models can substantially improve mortality forecasting in the given state (Khan et al., 2004). This motivates the problem of identifying interaction terms expressed as products of covariates of the form x_tx_{t −k} in other time series regression models including logistic regression for binary time series. This chapter discusses a spectral measure for interaction identification and its application in binary time series regression. The spectral measure for interaction identification, called residual coherence, depends on a certain nonlinear extension of the well-known measure of (squared) coherence. It is helpful, therefore, to provide first some background leading to the definition of residual coherence and illustrate its use. This is followed by an application to logistic regression for binary time series.