  The literature provides strong evidence that stock prices can be predicted
from past price data. Principal component analysis (PCA) is a widely used
mathematical technique for dimensionality reduction and analysis of data by
identifying a small number of principal components to explain the variation
found in a data set. In this paper, we describe a general method for stock
price prediction using covariance information, in terms of a dimension
reduction operation based on principle component analysis. Projecting the noisy
observation onto a principle subspace leads to a well-conditioned problem. We
illustrate our method on daily stock price values for five companies in
different industries. We investigate the results based on mean squared error
and directional change statistic of prediction, as measures of performance, and
volatility of prediction as a measure of risk.
