The literature provides strong evidence that stock price values can be predicted from past price data. Principal component analysis (PCA) identifies a small number of principle components that explain most of the variation in a data set. This method is often used for dimensionality reduction and analysis of the data. In this paper, we develop a general method for stock price prediction using time-varying covariance information. To address the time-varying nature of financial time series, we assign exponential weights to the price data so that recent data points are weighted more heavily. Our proposed method involves a dimension-reduction operation constructed based on principle components. Projecting the noisy observation onto a principle subspace results in a well-conditioned problem. We illustrate our results based on historical daily price data for 150 companies from different market-capitalization categories. We compare the performance of our method to two other methods: Gauss-Bayes, which is numerically demanding, and moving average, a simple method often used by technical traders and researchers. 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.