Classification Cramer-Rao bounds on stock price prediction

• Published in: Journal of forecasting 1998-09, Vol.17 (5-6), p.389-399
• Main Authors: Shin, Frances B., Kil, David H.
• Format: Article
• Language: English
• Subjects: class separability; Classification; cramer-Rao lower bound; Data analysis; Data compression; Estimating techniques; Forecasts; integrated pattern recognition; Parameter estimation; Performance evaluation; Stock prices; sufficient statistics
• ISSN: 0277-6693; 1099-131X
• DOI: 10.1002/(SICI)1099-131X(1998090)17:5/6<389::AID-FOR703>3.0.CO;2-N

In parameter estimation, we take advantage of the Cramer–Rao lower bound (CRLB) to evaluate the performance of estimation algorithms since the CRLB provides a theoretical upper bound on estimation accuracy. In pattern recognition, the same concept can be quite useful in terms of knowing the point of diminishing return. In this paper, we develop an innovative approach to quantifying the classification CRLB by combining the concepts of sufficient statistics and data compression with a metric that measures class separability. This approach allows us to assess the degree of performance optimality attained by each classifier. Instead of ranking performance of each classifier based on a confusion matrix, the proposed approach assigns a quantity called the optimality score that indicates the extent to which a classifier approximates the Bayes classifier. We illustrate the power of this approach with two interesting examples—two‐class prediction problems with known and unknown class‐conditional probability density functions. The latter case deals with prediction of S&P 500 price‐movement direction based on raw price data and technical indicators. Copyright © 1998 John Wiley & Sons, Ltd.