Functional Model Selection for Sparse Binary Time Series with Multiple Inputs

Consider an “output signal” recorded as a series of 0s and 1s, with 1 indicating that an event has occurred. An additional large set of observed “input signals” or potential covariates is available for modeling the probability of event occurrence. Of particular interest are binary input signals. Both input and output signals may be functions of either continuous or discrete time. Our analytic approach will treat time as continuous and employ tools from functional data analysis, though the actual data are usually recorded in discrete time.