Wavelet Neural Networks: With Applications in Financial Engineering, Chaos, and Classification

7 Modeling Uncertainty: From Point Estimates to Prediction Intervals

In earlier chapters a framework was presented where a wavelet network can efficiently be constructed, initialized, and trained. In this chapter we discuss the reliability of estimates of wavelet networks, since forecasts are characterized by uncertainty due to (1) inaccuracy in the measurements of the training data, and (2) limitations of the model. More precisely, in this chapter the framework proposed is expanded by presenting two methods for estimating confidence and prediction intervals.

The output of the wavelet network is the approximation of the underlying function f(x) obtained from the noisy data. In many applications, and especially in finance, risk managers may be more interested in predicting intervals for future movements of the underlying function f(x) than simply point estimates. For example, financial analysts who want to forecast the future movements of a stock are interested not only in the prices predicted but also in the confidence and prediction intervals. For example, if the price of a stock moves outside the prediction intervals, a financial analyst will take a position in the stock. If the price of the stock is below the lower bound, the stock is traded lower that it should be and a long position must be taken. On the other hand, if the price stock is above the upper bound of the prediction interval, the stock is too expensive and a short position should be taken.

In real data sets ...