Nonlinear time series prediction based on a power-law noise model

In this paper we investigate the influence of a power-law noise model, also called noise, on the performance of a feed-forward neural network used to predict time series. We introduce an optimization procedure that optimizes the parameters the neural networks by maximizing the likelihood function based on the power-law model. We show that our optimization procedure minimizes the mean squared leading to an optimal prediction. Further, we present numerical results applying method to time series from the logistic map and the annual number of sunspots demonstrate that a power-law noise model gives better results than a Gaussian model.

Extreme events and the morphodynamics of gravel-dominated coastal barriers: Strengthening uncertain ground

The long-term morphodynamic ordering of gravel-dominated coastal systems (GDCS), many of which serve as coastal defences in northwest Europe, is dominated by extreme events that generate barrier crest overflow. An understanding of this morphodynamic ordering is fraught with several unresolved difficulties. These are related to the twin problems of the inadequacy of pertinent morphodynamic parameterisation and of obtaining data from modern shores enabling such parameterisation. Major uncertainties concern the timing of over-crest flow in terms of return period of extreme elevation; the intensity and structure of the overflow field; antecedent beachface characteristics in response to storms; the rate of relative sea-level change; tidal stage control; and barrier resistance to forcing, itself determined by a number of unknowns including barrier form and size, sediment size and mosaics, and barrier resilience. While generalised extreme value modelling may provide a means of characterising overwashing return-period and its variability, exceptional tsunami events are outside the scope of such modelling. The characterisation of GDCS morphodynamics in terms of the forcing extreme events will necessitate integrating some or all of these parameters into a single model.