Forecasting high waters at Venice Lagoon using chaotic time series analisys and nonlinear neural netwoks

Time series analysis using nonlinear dynamics systems theory and multilayer neural networks models have been applied to the time sequence of water level data recorded every hour at 'Punta della Salute' from Venice Lagoon during the years 1980-1994. The first method is based on the reconstruction of the state space attractor using time delay embedding vectors and on the characterisation of invariant properties which define its dynamics. The results suggest the existence of a low dimensional chaotic attractor with a Lyapunov dimension, DL, of around 6.6 and a predictability between 8 and 13 hours ahead. Furthermore, once the attractor has been reconstructed it is possible to make predictions by mapping local-neighbourhood to local-neighbourhood in the reconstructed phase space. To compare the prediction results with another nonlinear method, two nonlinear autoregressive models (NAR) based on multilayer feedforward neural networks have been developed. From the study, it can be observed that nonlinear forecasting produces adequate results for the 'normal' dynamic behaviour of the water level of Venice Lagoon, outperforming linear algorithms, however, both methods fail to forecast the 'high water' phenomenon more than 2-3 hours ahead.Publicad

Psychic embedding — vision and delusion

The paper introduces the idea that the human brain may apply complex mathematical modules in order to process and understand the world. We speculate that the substrate of what appears outwardly as intuition, or prophetic power, may be a mathematical apparatus such as time-delay embedding. In this context, predictive accuracy may be the reflection of an appropriate choice of the embedding parameters. We further put this in the perspective of mental illness, and search for the possible differences between good intuition and delusive ideation. We speculate that the task at which delusional schizophrenic patients falter is not necessarily of perception, but rather of model selection. Failure of the psychotic patient to correctly choose the embedding parameters may readily lead to misinterpretation of an accurate perception through an altered reconstructed of the object perceived

Recurrence analysis techniques for non-stationary and non-linear data

When analysing food consumption data a number of problems arise when one departs from the comparative statics of conventional demand theory. Two of these properties, non-linearity and non-stationarity present a major challenge for econometric modelling. A new method for time series analysis, namely recurrence analysis, is outlined which allows for robust analysis of data that can not be satisfactorily handled with established econometric methods. The method is explained and applied to specific food consumption data. General implications for empirical modelling of similar data are inferred.