Which matrix decomposition technique is most effective in optimizing financial forecasting by reducing dimensionality while preserving essential information?

Principal Component Analysis (PCA) is usually the most effective matrix decomposition for financial forecasting because it transforms the original data matrix into a set of orthogonal components that capture the greatest variance with the fewest dimensions. The technique first centers the data, then computes the eigenvectors of the covariance matrix, and keeps only the leading eigenvectors whose eigenvalues explain most of the total variance. By projecting the high‑dimensional returns onto these few components, the model retains the essential patterns while discarding noise, which improves forecast stability and reduces over‑fitting. For example, if daily returns of five stocks are reduced to two principal components, the forecast model can use these two variables instead of five, saving computation time and improving accuracy. Thus, PCA balances dimensionality reduction with information preservation, making it ideal for financial forecasting.