This chapter gives an overview of the benchmark problems employed for assessing the prediction performance of the neural network models studied in this book. The first problem is a time series generated from the logistic map with intrinsic noise in the structural parameter α. This gives rise to a stochastic dynamical system that continually switches between the different regimes of fixedpoint behaviour, stable limit cycle and chaotic attractor. In the second problem, the noisy logistic map is stochastically coupled to a second stochastic dynamical system where, due to the stochastic coupling, bimodality of the conditional probability distribution arises. The third problem is taken from Ormoneit and Neuneier. A particle moves in a double-well potential subject to Brownian dynamics. The resulting time series shows fast oscillation around one of two metastable states and occasional phase transitions between these two states. As a consequence of the latter, long-term predictions require a model that can capture bimodality.
KeywordsBenchmark Problem Chaotic Attractor Stable Limit Cycle Intrinsic Noise Brownian Dynamic
Unable to display preview. Download preview PDF.