Summary: Estimating Model Limitation in Financial
Markets
Malik Magdon­Ismail 1 , Alexander Nicholson 2 and Yaser Abu­Mostafa 3
1 malik@work.caltech.edu
2 zander@work.caltech.edu
3 yaser@caltech.edu
Learning Systems Group, California Institute of Technology
136­93 Caltech, Pasadena, CA, USA, 91125
Abstract. We introduce bounds on the generalization ability when learn­
ing with noisy data. These results quantify the trade­off between the
amount of data and the noise level in the data. Our results can be used
to derive a method for estimating the model limitation for a given learn­
ing problem. Changes in model imitation can then be used to detect a
change in market volatility. Our results apply to linear as well as nonlin­
ear models and algorithms, and to different noise models. We successfully
apply our methods to the four major foreign exchange markets.
1 Introduction
Learning from financial data entails the extraction of relevant information from
overwhelming noise. Financial markets are dynamic systems so the noise param­
eters may fluctuate with time. In addition to being a nuisance that complicates

Source: Abu-Mostafa, Yaser S. - Department of Mechanical Engineering & Computer Science Department, California Institute of Technology
Magdon-Ismail, Malik - Department of Computer Science, Rensselaer Polytechnic Institute

Collections: Computer Technologies and Information Sciences