title: Granger causality analysis with nonuniform sampling and its application to pulse-coupled nonlinear dynamics.
abstract: The Granger causality (GC) analysis is an effective approach to infer causal relations for time series. However, for data obtained by uniform sampling (i.e., with an equal sampling time interval), it is known that GC can yield unreliable causal inference due to aliasing if the sampling rate is not sufficiently high. To solve this unreliability issue, we consider the nonuniform sampling scheme as it can mitigate against aliasing. By developing an unbiased estimation of power spectral density of nonuniformly sampled time series, we establish a framework of spectrum-based nonparametric GC analysis. Applying this framework to a general class of pulse-coupled nonlinear networks and utilizing some particular spectral structure possessed by these nonlinear network data, we demonstrate that, for such nonlinear networks with nonuniformly sampled data, reliable GC inference can be achieved at a low nonuniform mean sampling rate at which the traditional uniform sampling GC may lead to spurious causal inference.
authors.affiliation: Department of Mathematics, MOE-LSC, and Institute of Natural Sciences, Shanghai Jiao Tong University, Shanghai, China.
authors.forename: Yaoyu
authors.initials: Y
authors.lastname: Zhang
authors.affiliation: Department of Mathematics, MOE-LSC, and Institute of Natural Sciences, Shanghai Jiao Tong University, Shanghai, China.
authors.forename: Yanyang
authors.initials: Y
authors.lastname: Xiao
authors.affiliation: Department of Mathematics, MOE-LSC, and Institute of Natural Sciences, Shanghai Jiao Tong University, Shanghai, China.
authors.forename: Douglas
authors.initials: D
authors.lastname: Zhou
authors.affiliation: Department of Mathematics, MOE-LSC, and Institute of Natural Sciences, Shanghai Jiao Tong University, Shanghai, China.|Courant Institute of Mathematical Sciences and Center for Neural Science, New York University, New York, New York 10012, USA.|NYUAD Institute, New York University Abu Dhabi, Abu Dhabi, United Arab Emirates.
authors.forename: David
authors.initials: D
authors.lastname: Cai