The multilayer perceptron model has been suggested as an alternative to conventional approaches, and can accurately forecast time series. Additionally, several novel artificial neural network models have been proposed as alternatives to the multilayer perceptron model, which have used (for example) the generalized- mean, geometric mean, and multiplicative neuron models. Although all of these artificial neural network models can produce successful forecasts, their aggregation functions mean that they are negatively affected by outliers. In this study, we propose a new multilayer, feed forward neural network model, which is a robust model that uses the trimmed mean neuron model. Its aggregation function does not depend on outliers. We trained this multilayer, feed forward neural network using modied particle swarm optimization. We applied the proposed method to three well-known time series, and our results suggest that it produces superior forecasts when compared with similar methods.
Kohonen's self-organizing maps are a recognized tool for finding representative data vectors and clustering the data. To what extent is it possible to preserve the topology of the data in the constructed planar map? We address the question looking at distal data points located at the peripherals of the data cloud and their position in the provided map. Several data sets have been investigated; we present the results for two of them: the Glass data (dimension d=7) and the Ionosphere data (dimension d=32). It was found that the distal points are reproduced either at the edges (borders) of the map, or at the peripherals of dark regions visualized in the maps.
Recursive time series methods are very popular due to their numerical simplicity. Their theoretical background is usually based on Kalman filtering in state space models (mostly in dynamic linear systems). However, in time series practice one must face frequently to outlying values (outliers), which require applying special methods of robust statistics. In the paper a simple robustification of Kalman filter is suggested using a simple truncation of the recursive residuals. Then this concept is applied mainly to various types of exponential smoothing (recursive estimation in Box-Jenkins models with outliers is also mentioned). The methods are demonstrated using simulated data.