Financial markets: very noisy information processing

We report new results about the impact of noise on information processing with application to financial markets. These results quantify the trade-off between the amount of data and the noise level in the data. They also provide estimates for the performance of a learning system in terms of the noise level. We use these results to derive a method for detecting the change in market volatility from period to period. We successfully apply these results to the four major foreign exchange markets. The results hold for linear as well as nonlinear learning models and algorithms and for different noise models.