The validation of causal relationship between two groups of multivariate time series data often requires the precedence knowledge of all variables. However, in practice one finds that some variables may be negligible in describing the underlying causal structure. In this article we provide an...

In this paper, the methods of time series for nonlinearity are briefly surveyed, with particular attention paid to a new test design based on a neural network specification. The proposed integrated expert system contains two main components: an identification environment and a robust forecasting...

Kernel-type estimators of the multivariate density of stationary random fields indexed by multidimensional lattice points space are investigated. Sufficient conditions for kernel estimators to converge uniformly are obtained. The estimators can attain the optimal rates L[infinity] of...