In this paper a numerically robust lattice-ladder learning algorithm is presented that sequentially selects the best specification of a subset time series system using neural networks. We have been able to extend the relevance of multilayered neural networks and so more effectively model a greater array of time series situations. We have recognized that many connections between nodes in layers are unnecessary and can be deleted. So we have introduced inhibitor arcs, reflecting inhibitive synapses. We also allow for connections between nodes in layers which have variable strengths at different points of time by introducing additionally excitatory arcs, reflecting excitatory synapses. The resolving of both time and order updating leads to optimal synaptic weight updating and allows for optimal dynamic node creation/deletion within the extended neural network. The paper presents two applications that demonstrate the usefulness of the process.